Richard H. Rand - Author Profile

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Rand, Richard H.

Author ID:	rand.richard-h
Published as:	Rand, Richard H.; Rand, Richard; Rand, R. H.; Rand, R. more...less

Documents Indexed:	137 Publications since 1967, including 3 Books and 3 Additional arXiv Preprints
	1 Further Contribution
Biographic References:	1 Publication
Co-Authors:	88 Co-Authors with 119 Joint Publications
	1,078 Co-Co-Authors

all top 5

Co-Authors

13	single-authored
10	Wesson, Elizabeth N.
8	Pender, Jamol J.
6	Sah, Si Mohamed
5	Coppola, Vincent T.
5	Storti, Duane W.
5	Vakakis, Alexander F.
5	Verdugo, Anael
5	Zounes, Randolph S.
4	Keith, William L.
4	Ng, Leslie
4	Zehnder, Alan T.
3	Belhaq, Mohamed
3	Bridge, Jacqueline
3	Heckman, Christoffer R.
3	Month, Leslie Anne
3	Morrison, Tina M.
3	Recktenwald, Geoffrey
3	Ruelas, Rocio E.
3	Shayak, B.
3	Sheheitli, Hiba
3	Suchorsky, Meghan Kathleen
3	Tseng, Shoei-Fu
2	Abouhazim, Nazha
2	Bhaskar, Aditya
2	Chakraborty, Tapesh
2	Cooke, J. R.
2	Guckenheimer, John M.
2	Haberman, Richard
2	Hastings, Rachel
2	Holmes, Philip J.
2	Howland, Howard
2	Kinsey, R. J.
2	Kovacic, Ivana
2	Len, Jonathan L.
2	Mendelowitz, Lee
2	Mingori, D. Lewis
2	Moon, Francis C.
2	Niklas, K. J.
2	Novitzky, Sophia
2	Pandey, Manoj Kumar
2	Quinn, D. Dane
2	Ramani, Deepak V.
2	Rand, David G.
2	Schlomiuk, Dana I.
2	Upadhyaya, Shrinivasa K.
2	Wirkus, Stephen A.
1	Adaricheva, Kira Vladislavovna
1	Alfriend, Kyle T.
1	Armbruster, Dieter
1	Barcilon, Albert
1	Bernstein, Alexander
1	Block, Henry David
1	Camacho, Erika T.
1	Cao, Shiping
1	Caswell, Hal
1	Chati, M.
1	Cohen, Avis H.
1	Coniglio, Anthony
1	Davidow, Matthew
1	de Wolff, Babette A. J.
1	Dercole, Fabio
1	DiMaggio, Frank L.
1	Doldo, Philip
1	Ellenson, J. L.
1	Fiedler, Bernold
1	Gilmour, Robert F. jun.
1	Gladman, Brett
1	Gluzman, Mark O.
1	Golnaraghi, M. Farid
1	Gross, Louis J.
1	Guennoun, Kamar
1	Holmes, Catherine A.
1	Johnson, I. R.
1	Johnson, Timothy Lee
1	Kotas, Jakob
1	Lakrad, Faouzi
1	Lewis, Donald C.
1	Li, Guangxuan
1	Lubkin, Sharon R.
1	Miura, Robert M.
1	Mukherjee, Subrata
1	Nation, James B.
1	Newman, A. L.
1	Newman, William I.
1	Nicholson, Phil
1	Nieto, Alejandro López
1	Niu, Xueyan
1	O’Neil, Michael
1	Rompala, Kevin
1	Roughgarden, Joan
1	Rozhkov, Igor
1	Ruina, Andy L.
1	Schneider, Isabelle
1	Sen, Asok K.
1	Shaw, Steven W.
1	Strichartz, Robert Stephen
1	Stubna, Michael D.
1	Thornley, John H. M.
1	Wong, Jeffrey T.
1	Woods, Steven D.
...and 2 more Co-Authors

all top 5

Serials

22	International Journal of Non-Linear Mechanics
21	Nonlinear Dynamics
17	Communications in Nonlinear Science and Numerical Simulation
7	Journal of Mathematical Biology
6	Journal of Applied Mechanics
6	Journal of Applied Nonlinear Dynamics
4	Mechanics Research Communications
3	Acta Mechanica
3	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
3	Journal of Vibration and Control
2	Journal of the Acoustical Society of America
2	SIAM Journal on Applied Mathematics
2	Communications on Pure and Applied Analysis
2	SIAM Journal on Applied Dynamical Systems
1	AIAA Journal
1	Discrete Applied Mathematics
1	International Journal of Solids and Structures
1	Journal of Sound and Vibration
1	Nonlinearity
1	Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
1	Chaos, Solitons and Fractals
1	Journal of Guidance, Control and Dynamics
1	Applied Mathematics and Computation
1	Journal of Differential Equations
1	Mathematics of Operations Research
1	Dynamics and Stability of Systems
1	Queueing Systems
1	Expositiones Mathematicae
1	Celestial Mechanics and Dynamical Astronomy
1	Journal of Difference Equations and Applications
1	European Series in Applied and Industrial Mathematics (ESAIM): Proceedings
1	Chaos
1	Applied Mathematical Sciences
1	Lectures on Mathematics in the Life Sciences
1	The College Mathematics Journal
1	Dynamic Games and Applications
1	Research Notes in Mathematics (San Francisco)

all top 5

Fields

68	Ordinary differential equations (34-XX)
54	Mechanics of particles and systems (70-XX)
21	Dynamical systems and ergodic theory (37-XX)
16	Biology and other natural sciences (92-XX)
8	Computer science (68-XX)
7	Mechanics of deformable solids (74-XX)
7	Operations research, mathematical programming (90-XX)
5	Game theory, economics, finance, and other social and behavioral sciences (91-XX)
4	Partial differential equations (35-XX)
4	Numerical analysis (65-XX)
3	Fluid mechanics (76-XX)
2	Special functions (33-XX)
2	Probability theory and stochastic processes (60-XX)
2	Systems theory; control (93-XX)
1	Mathematical logic and foundations (03-XX)
1	Order, lattices, ordered algebraic structures (06-XX)
1	Measure and integration (28-XX)
1	Difference and functional equations (39-XX)
1	Integral equations (45-XX)
1	Statistics (62-XX)
1	Optics, electromagnetic theory (78-XX)
1	Statistical mechanics, structure of matter (82-XX)

Publications by Year

all cited Publications top 5 cited Publications

Citations contained in zbMATH Open

119 Publications have been cited 1,161 times in 803 Documents	Cited by ▼	Year ▼
Perturbation methods, bifurcation theory and computer algebra. Zbl 0651.34001 Rand, Richard H.; Armbruster, Dieter	67	1987
The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model. Zbl 0476.92003 Cohen, Avis H.; Holmes, Philip J.; Rand, Richard H.	62	1982
Bifurcation of periodic motions in two weakly coupled van der Pol oscillators. Zbl 0447.70028 Rand, R. H.; Holmes, P. J.	56	1980
The dynamics of two coupled van der Pol oscillators with delay coupling. Zbl 1021.70010 Wirkus, Stephen; Rand, Richard	48	2002
The transition to chaos in a simple mechanical system. Zbl 0666.70030 Shaw, Steven W.; Rand, Richard H.	40	1989
Computer algebra in applied mathematics: an introduction to MACSYMA. Zbl 0583.68012 Rand, R. H.	38	1984
Dynamics of three coupled van der Pol oscillators with application to circadian rhythms. Zbl 1120.34025 Rompala, Kevin; Rand, Richard; Howland, Howard	31	2007
Averaging using elliptic functions: Approximation of limit cycles. Zbl 0699.34032 Coppola, V. T.; Rand, R. H.	31	1990
Transition curves for the quasi-periodic Mathieu equation. Zbl 0916.34031 Zounes, Randolph S.; Rand, Richard H.	30	1998
The transition from phase locking to drift in a system of two weakly coupled Van Der Pol oscillators. Zbl 0667.70028 Chakraborty, Tapesh; Rand, Richard H.	27	1988
Queues with choice via delay differential equations. Zbl 1366.90082 Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth	26	2017
Dynamics of two van der Pol oscillators coupled via a bath. Zbl 1052.70013 Camacho, Erika; Rand, Richard; Howland, Howard	23	2004
Integrability of plane quadratic vector fields. Zbl 0693.34030 Schlomiuk, Dana; Guckenheimer, John; Rand, Richard	23	1990
Bifurcations in a Mathieu equation with cubic nonlinearities. Zbl 1029.70009 Ng, Leslie; Rand, Richard	22	2002
2:2:1 resonance in the quasiperiodic Mathieu equation. Zbl 1062.70596 Rand, Richard; Guennoun, Kamar; Belhaq, Mohamed	21	2003
Dynamics of two strongly coupled van der Pol oscillators. Zbl 0498.70037 Storti, D. W.; Rand, R. H.	21	1982
Ordered direct implicational basis of a finite closure system. Zbl 1288.06007 Adaricheva, K.; Nation, J. B.; Rand, R.	21	2013
Hopf bifurcation in a DDE model of gene expression. Zbl 1134.34325 Verdugo, Anael; Rand, Richard	20	2008
Hopf bifurcation formula for first order differential-delay equations. Zbl 1123.34334 Rand, Richard; Verdugo, Anael	20	2007
An analysis of queues with delayed information and time-varying arrival rates. Zbl 1392.90055 Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth	20	2018
\(2:1\) Resonance in the delayed nonlinear Mathieu equation. Zbl 1193.70031 Morrison, Tina M.; Rand, Richard H.	17	2007
Global behavior of a nonlinear quasiperiodic Mathieu equation. Zbl 1003.34041 Zounes, Randolph S.; Rand, Richard H.	17	2002
Modal analysis of a cracked beam. Zbl 1235.74056 Chati, M.; Rand, R.; Mukherjee, S.	16	1997
Bifurcations and chaos in a forced zero-stiffness impact oscillator. Zbl 0714.73049 Li, G. X.; Rand, R. H.; Moon, F. C.	15	1990
Nonlinear dynamics in queueing theory: determining the size of oscillations in queues with delay. Zbl 1417.34202 Novitzky, Sophia; Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth	14	2019
Dynamics of spinup through resonance. Zbl 0825.70085 Rand, R. H.; Kinsey, R. J.; Mingori, D. L.	14	1992
Hopf bifurcations in delayed rock-paper-scissors replicator dynamics. Zbl 1348.91051 Wesson, Elizabeth; Rand, Richard	13	2016
Normal modes and global dynamics of a two-degree-of-freedom non-linear system. I: Low energies. Zbl 0765.70014 Vakakis, A. F.; Rand, R. H.	13	1992
Subharmonic resonance in the nonlinear Mathieu equation. Zbl 1116.34322 Zounes, Randolph S.; Rand, Richard H.	13	2002
Frequency locking in a forced Mathieu–Van der Pol–Duffing system. Zbl 1279.34042 Pandey, Manoj; Rand, Richard H.; Zehnder, Alan T.	13	2008
A direct method for non-linear normal modes. Zbl 0296.70021 Rand, Richard H.	12	1974
A pair of van der Pol oscillators coupled by fractional derivatives. Zbl 1258.34074 Suchorsky, M. K.; Rand, R. H.	12	2012
A stochastic analysis of queues with customer choice and delayed information. Zbl 1466.60190 Pender, Jamol; Rand, Richard; Wesson, Elizabeth	12	2020
Perturbation analysis of entrainment in a micromechanical limit cycle oscillator. Zbl 1124.34026 Pandey, Manoj; Rand, Richard; Zehnder, Alan	12	2007
Analytical approximation for period-doubling following a Hopf bifurcation. Zbl 0684.58030 Rand, Richard H.	12	1989
Limiting the oscillations in queues with delayed information through a novel type of delay announcement. Zbl 1455.34086 Novitzky, Sophia; Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth	11	2020
Dynamics of two strongly coupled relaxation oscillators. Zbl 0589.34043 Storti, D. W.; Rand, R. H.	10	1986
Topics in nonlinear dynamics with computer algebra. Zbl 0853.70001 Rand, Richard H.	10	1994
Non-linear dynamics of a system of coupled oscillators with essential stiffness non-linearities. Zbl 1348.34073 Vakakis, Alexander F.; Rand, Richard H.	10	2004
\(2:1:1\) resonance in the quasi-periodic Mathieu equation. Zbl 1132.34041 Rand, Richard; Morrison, Tina	10	2005
Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems. Zbl 0677.58038 Guckenheimer, John; Rand, Richard; Schlomiuk, Dana	10	1989
Hopf bifurcations in two-strategy delayed replicator dynamics. Zbl 1334.34180 Wesson, Elizabeth; Rand, Richard; Rand, David	9	2016
A simplified model of coupled relaxation oscillators. Zbl 0614.73024 Storti, Duane; Rand, Richard H.	9	1987
Bifurcations in a Mathieu equation with cubic nonlinearities. II. Zbl 1043.34040 Ng, Leslie; Rand, Richard	9	2002
Center manifold analysis of a DDE model of gene expression. Zbl 1221.37197 Verdugo, Anael; Rand, Richard	9	2008
Dynamics of three coupled limit cycle oscillators with application to artificial intelligence. Zbl 1221.34099 Mendelowitz, Lee; Verdugo, Anael; Rand, Richard	9	2009
Using delay to quench undesirable vibrations. Zbl 1218.34085 Suchorsky, M. K.; Sah, S. M.; Rand, R. H.	8	2010
Stability of the triangular points in the elliptic restricted problem of three bodies. Zbl 0179.53203 Alfriend, K. T.; Rand, R. H.	8	1969
How to pump a swing. Zbl 0995.70502 Wirkus, Stephen; Rand, Richard; Ruina, Andy	8	1998
Nonlinear effects on coexistence phenomenon in parametric excitation. Zbl 1026.70024 Ng, Leslie; Rand, Richard	7	2003
A higher order approximation for non-linear normal modes in two degree of freedom systems. Zbl 0223.34019 Rand, Richard H.	7	1971
Vibrations of fluid-filled spherical and spheroidal shells. Zbl 0161.44304 Rand, R.; DiMaggio, F.	7	1967
Analysis of a nonlinear partial difference equation, and its application to cardiac dynamics. Zbl 1012.39004 Stubna, Michael D.; Rand, Richard H.; Gilmour, Robert F. jun.	7	2002
Normal modes and global dynamics of a two-degree-of-freedom non-linear system. II: High energies. Zbl 0765.70015 Vakakis, A. F.; Rand, R. H.	7	1992
Dynamics of a system exhibiting the global bifurcation of a limit cycle at infinity. Zbl 0647.34033 Keith, W. L.; Rand, R. H.	7	1985
Dynamics of four coupled phase-only oscillators. Zbl 1122.70015 Rand, Richard; Wong, Jeffrey	7	2008
Perturbation solution for secondary bifurcation in the quadratically-damped Mathieu equation. Zbl 1348.34059 Ramani, Deepak V.; Keith, William L.; Rand, Richard H.	7	2004
Straight-line backbone curve. Zbl 1304.34071 Kovacic, Ivana; Rand, Richard	6	2013
Coexistence of infinitely many large, stable, rapidly oscillating periodic solutions in time-delayed Duffing oscillators. Zbl 1443.34070 Fiedler, Bernold; Nieto, Alejandro López; Rand, Richard H.; Sah, Si Mohamed; Schneider, Isabelle; de Wolff, Babette	6	2020
Differential-delay equations. Zbl 1253.34065 Rand, Richard	6	2011
Evolutionary dynamics of a system with periodic coefficients. Zbl 1217.91018 Rand, Richard H.; Yazhbin, Max; Rand, David G.	6	2011
A quasiperiodic Mathieu equation. Zbl 0918.34033 Rand, Richard; Zounes, Randolph; Hastings, Rachel	6	1995
A numerical investigation of the dynamics of a system of two time-delay coupled relaxation oscillators. Zbl 1056.34082 Sen, Asok K.; Rand, Richard H.	5	2003
Dynamics of microbubble oscillators with delay coupling. Zbl 1268.34073 Heckman, C. R.; Rand, R. H.	5	2013
Self-thinning and community persistence in a simple size-structured dynamical model of plant growth. Zbl 1086.92036 Dercole, F.; Niklas, K.; Rand, R.	5	2005
Nonlinear control of dual-spin spacecraft during despin through precession phase lock. Zbl 0855.93057 Kinsey, R. J.; Mingori, D. L.; Rand, R. H.	5	1996
Bifurcation of nonlinear normal modes in a class of two degree of freedom systems. Zbl 0793.70014 Rand, R. H.; Pak, C. H.; Vakakis, A. F.	5	1992
Dynamics of a ring of three coupled relaxation oscillators. Zbl 1221.34094 Bridge, J.; Mendelowitz, L.; Rand, R.; Sah, S.; Verdugo, A.	5	2009
1:1 and 2:1 phase entrainment in a system of two coupled limit cycle oscillators. Zbl 0547.92001 Keith, W. L.; Rand, R. H.	5	1984
On the existence and bifurcation of minimal normal modes. Zbl 0421.70029 Johnson, T. L.; Rand, R. H.	5	1979
About a class of nonlinear oscillators with amplitude-independent frequency. Zbl 1281.34050 Kovacic, Ivana; Rand, Richard	4	2013
An application of the Poincaré map to the stability of nonlinear normal modes. Zbl 0449.70021 Month, L. A.; Rand, R. H.	4	1980
Breaking the symmetry in queues with delayed information. Zbl 1470.90023 Doldo, Philip; Pender, Jamol; Rand, Richard	4	2021
Parametric resonance of Hopf bifurcation. Zbl 1096.70011 Rand, Richard; Barcilon, Albert; Morrison, Tina	4	2005
Oscillatory reaction-diffusion equations on rings. Zbl 0802.92002 Lubkin, Sharon; Rand, Richard	4	1994
Resonant capture in a system of two coupled homoclinic oscillators. Zbl 0949.34506 Rand, R. H.; Quinn, D. D.	4	1995
Determinacy of degenerate equilibria with linear part \(x'=y\), \(y'=0\) using MACSYMA. Zbl 0624.65068 Rand, R. H.; Keith, W. L.	4	1987
Coexistence phenomenon in autoparametric excitation of two degree of freedom systems. Zbl 1349.70044 Recktenwald, Geoffrey; Rand, Richard	4	2005
Slow passage through resonance in Mathieu’s equation. Zbl 1053.70009 Ng, Leslie; Rand, Richard; O’Neil, Michael	3	2003
The geometrical stability of non-linear normal modes in two degree of freedom systems. Zbl 0264.70022 Rand, Richard H.	3	1973
Torsional vibrations of elastic prolate spheroids. Zbl 0164.26804 Rand, R. H.	3	1968
Resonant capture and separatrix crossing in dual-spin spacecraft. Zbl 0941.70021 Haberman, Richard; Rand, Richard; Yuster, Thomas	3	1999
Three oscillator model of the heartbeat generator. Zbl 1221.34102 Suchorsky, Meghan; Rand, Richard	3	2009
Perturbation methods and computer algebra in mechanics. Zbl 0828.73080 Rand, R. H.	3	1994
MACSYMA program to implement averging using elliptic functions. Zbl 0741.65055 Coppola, Vincent T.; Rand, Richard H.	3	1991
Computer algebra implementation of Lie transforms for Hamiltonian systems: Application to the nonlinear stability of \(L_ 4\). Zbl 0696.70015 Coppola, V. T.; Rand, R. H.	3	1989
Asymptotic analysis of the Hopf-Hopf bifurcation in a time-delay system. Zbl 1304.34124 Heckman, Christoffer R.; Rand, Richard H.	2	2012
Alternate models of replicator dynamics. Zbl 1300.92065 Wesson, Elizabeth N.; Rand, Richard H.	2	2013
Slow passage through multiple parametric resonance tongues. Zbl 1273.70039 Bridge, Jacqueline; Rand, Richard; Sah, Si Mohamed	2	2009
Dynamics of three coupled limit cycle oscillators with vastly different frequencies. Zbl 1280.34044 Sheheitli, Hiba; Rand, Richard H.	2	2011
Hopf bifurcation in a stomatal oscillator. Zbl 0467.92005 Rand, R. H.; Upadhyaya, S. K.; Cooke, J. R.; Storti, D. W.	2	1981
Coupled oscillators as a model for nonlinear parametric excitation. Zbl 0489.70018 Holmes, Catherine A.; Rand, Richard H.	2	1981
Bifurcation of 4:1 subharmonics in the nonlinear Mathieu equation. Zbl 0501.70028 Month, Leslie Anne; Rand, Richard H.	2	1982
Dynamics of a mass-spring-pendulum system with vastly different frequencies. Zbl 1267.34065 Sheheitli, Hiba; Rand, Richard H.	2	2012
Dynamics of a nonlinear parametrically-excited PDE: 2-term truncation. Zbl 0868.35007 Rand, Richard H.	2	1996
The damped nonlinear quasiperiodic Mathieu equation near 2:2:1 resonance. Zbl 1141.70011 Abouhazim, Nazha; Rand, Richard H.; Belhaq, Mohamed	2	2006
Nonlinear normal modes in a system with nonholonomic constraints. Zbl 1004.70009 Rand, R. H.; Ramani, D. V.	2	2001
Fluid mechanics of green plants. Zbl 0564.76128 Rand, Richard H.	2	1983
Origin of arrhythmias in a heart model. Zbl 1221.37193 Sheheitli, Hiba; Rand, Richard	2	2009
Delay terms in the slow flow. Zbl 1356.70031 Sah, Si Mohamed; Rand, Richard H.	2	2016
Breaking the symmetry in queues with delayed information. Zbl 1470.90023 Doldo, Philip; Pender, Jamol; Rand, Richard	4	2021
A stochastic analysis of queues with customer choice and delayed information. Zbl 1466.60190 Pender, Jamol; Rand, Richard; Wesson, Elizabeth	12	2020
Limiting the oscillations in queues with delayed information through a novel type of delay announcement. Zbl 1455.34086 Novitzky, Sophia; Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth	11	2020
Coexistence of infinitely many large, stable, rapidly oscillating periodic solutions in time-delayed Duffing oscillators. Zbl 1443.34070 Fiedler, Bernold; Nieto, Alejandro López; Rand, Richard H.; Sah, Si Mohamed; Schneider, Isabelle; de Wolff, Babette	6	2020
The Mathieu differential equation and generalizations to infinite fractafolds. Zbl 1454.34049 Cao, Shiping; Coniglio, Anthony; Niu, Xueyan; Rand, Richard H.; Strichartz, Robert S.	1	2020
Nonlinear dynamics in queueing theory: determining the size of oscillations in queues with delay. Zbl 1417.34202 Novitzky, Sophia; Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth	14	2019
An analysis of queues with delayed information and time-varying arrival rates. Zbl 1392.90055 Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth	20	2018
Queues with choice via delay differential equations. Zbl 1366.90082 Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth	26	2017
Hopf bifurcations in delayed rock-paper-scissors replicator dynamics. Zbl 1348.91051 Wesson, Elizabeth; Rand, Richard	13	2016
Hopf bifurcations in two-strategy delayed replicator dynamics. Zbl 1334.34180 Wesson, Elizabeth; Rand, Richard; Rand, David	9	2016
Delay terms in the slow flow. Zbl 1356.70031 Sah, Si Mohamed; Rand, Richard H.	2	2016
Disappearance of resonance tongues. Zbl 1320.70017 Ruelas, Rocio E.; Rand, Richard H.	1	2015
Ordered direct implicational basis of a finite closure system. Zbl 1288.06007 Adaricheva, K.; Nation, J. B.; Rand, R.	21	2013
Straight-line backbone curve. Zbl 1304.34071 Kovacic, Ivana; Rand, Richard	6	2013
Dynamics of microbubble oscillators with delay coupling. Zbl 1268.34073 Heckman, C. R.; Rand, R. H.	5	2013
About a class of nonlinear oscillators with amplitude-independent frequency. Zbl 1281.34050 Kovacic, Ivana; Rand, Richard	4	2013
Alternate models of replicator dynamics. Zbl 1300.92065 Wesson, Elizabeth N.; Rand, Richard H.	2	2013
Center manifold reduction of the Hopf-Hopf bifurcation in a time delay system. Zbl 1330.34111 Heckman, Christoffer; Kotas, Jakob; Rand, Richard	1	2013
A pair of van der Pol oscillators coupled by fractional derivatives. Zbl 1258.34074 Suchorsky, M. K.; Rand, R. H.	12	2012
Asymptotic analysis of the Hopf-Hopf bifurcation in a time-delay system. Zbl 1304.34124 Heckman, Christoffer R.; Rand, Richard H.	2	2012
Dynamics of a mass-spring-pendulum system with vastly different frequencies. Zbl 1267.34065 Sheheitli, Hiba; Rand, Richard H.	2	2012
Differential-delay equations. Zbl 1253.34065 Rand, Richard	6	2011
Evolutionary dynamics of a system with periodic coefficients. Zbl 1217.91018 Rand, Richard H.; Yazhbin, Max; Rand, David G.	6	2011
Dynamics of three coupled limit cycle oscillators with vastly different frequencies. Zbl 1280.34044 Sheheitli, Hiba; Rand, Richard H.	2	2011
Using delay to quench undesirable vibrations. Zbl 1218.34085 Suchorsky, M. K.; Sah, S. M.; Rand, R. H.	8	2010
Dynamics of a model of two delay-coupled relaxation oscillators. Zbl 1222.37019 Ruelas, R. E.; Rand, R. H.	1	2010
Dynamics of three coupled limit cycle oscillators with application to artificial intelligence. Zbl 1221.34099 Mendelowitz, Lee; Verdugo, Anael; Rand, Richard	9	2009
Dynamics of a ring of three coupled relaxation oscillators. Zbl 1221.34094 Bridge, J.; Mendelowitz, L.; Rand, R.; Sah, S.; Verdugo, A.	5	2009
Three oscillator model of the heartbeat generator. Zbl 1221.34102 Suchorsky, Meghan; Rand, Richard	3	2009
Slow passage through multiple parametric resonance tongues. Zbl 1273.70039 Bridge, Jacqueline; Rand, Richard; Sah, Si Mohamed	2	2009
Origin of arrhythmias in a heart model. Zbl 1221.37193 Sheheitli, Hiba; Rand, Richard	2	2009
Dynamics of a ring network of phase-only oscillators. Zbl 1221.34095 Bridge, Jacqueline; Rand, Richard; Sah, Si Mohamed	1	2009
Hopf bifurcation in a DDE model of gene expression. Zbl 1134.34325 Verdugo, Anael; Rand, Richard	20	2008
Frequency locking in a forced Mathieu–Van der Pol–Duffing system. Zbl 1279.34042 Pandey, Manoj; Rand, Richard H.; Zehnder, Alan T.	13	2008
Center manifold analysis of a DDE model of gene expression. Zbl 1221.37197 Verdugo, Anael; Rand, Richard	9	2008
Dynamics of four coupled phase-only oscillators. Zbl 1122.70015 Rand, Richard; Wong, Jeffrey	7	2008
Dynamics of three coupled van der Pol oscillators with application to circadian rhythms. Zbl 1120.34025 Rompala, Kevin; Rand, Richard; Howland, Howard	31	2007
Hopf bifurcation formula for first order differential-delay equations. Zbl 1123.34334 Rand, Richard; Verdugo, Anael	20	2007
\(2:1\) Resonance in the delayed nonlinear Mathieu equation. Zbl 1193.70031 Morrison, Tina M.; Rand, Richard H.	17	2007
Perturbation analysis of entrainment in a micromechanical limit cycle oscillator. Zbl 1124.34026 Pandey, Manoj; Rand, Richard; Zehnder, Alan	12	2007
Stability of strongly nonlinear normal modes. Zbl 1165.34378 Recktenwald, Geoffrey; Rand, Richard	1	2007
Trigonometric simplification of a class of conservative nonlinear oscillators. Zbl 1187.70037 Recktenwald, Geoffrey; Rand, Richard	1	2007
The damped nonlinear quasiperiodic Mathieu equation near 2:2:1 resonance. Zbl 1141.70011 Abouhazim, Nazha; Rand, Richard H.; Belhaq, Mohamed	2	2006
\(2:1:1\) resonance in the quasi-periodic Mathieu equation. Zbl 1132.34041 Rand, Richard; Morrison, Tina	10	2005
Self-thinning and community persistence in a simple size-structured dynamical model of plant growth. Zbl 1086.92036 Dercole, F.; Niklas, K.; Rand, R.	5	2005
Parametric resonance of Hopf bifurcation. Zbl 1096.70011 Rand, Richard; Barcilon, Albert; Morrison, Tina	4	2005
Coexistence phenomenon in autoparametric excitation of two degree of freedom systems. Zbl 1349.70044 Recktenwald, Geoffrey; Rand, Richard	4	2005
Dynamics of two van der Pol oscillators coupled via a bath. Zbl 1052.70013 Camacho, Erika; Rand, Richard; Howland, Howard	23	2004
Non-linear dynamics of a system of coupled oscillators with essential stiffness non-linearities. Zbl 1348.34073 Vakakis, Alexander F.; Rand, Richard H.	10	2004
Perturbation solution for secondary bifurcation in the quadratically-damped Mathieu equation. Zbl 1348.34059 Ramani, Deepak V.; Keith, William L.; Rand, Richard H.	7	2004
2:2:1 resonance in the quasiperiodic Mathieu equation. Zbl 1062.70596 Rand, Richard; Guennoun, Kamar; Belhaq, Mohamed	21	2003
Nonlinear effects on coexistence phenomenon in parametric excitation. Zbl 1026.70024 Ng, Leslie; Rand, Richard	7	2003
A numerical investigation of the dynamics of a system of two time-delay coupled relaxation oscillators. Zbl 1056.34082 Sen, Asok K.; Rand, Richard H.	5	2003
Slow passage through resonance in Mathieu’s equation. Zbl 1053.70009 Ng, Leslie; Rand, Richard; O’Neil, Michael	3	2003
The dynamics of two coupled van der Pol oscillators with delay coupling. Zbl 1021.70010 Wirkus, Stephen; Rand, Richard	48	2002
Bifurcations in a Mathieu equation with cubic nonlinearities. Zbl 1029.70009 Ng, Leslie; Rand, Richard	22	2002
Global behavior of a nonlinear quasiperiodic Mathieu equation. Zbl 1003.34041 Zounes, Randolph S.; Rand, Richard H.	17	2002
Subharmonic resonance in the nonlinear Mathieu equation. Zbl 1116.34322 Zounes, Randolph S.; Rand, Richard H.	13	2002
Bifurcations in a Mathieu equation with cubic nonlinearities. II. Zbl 1043.34040 Ng, Leslie; Rand, Richard	9	2002
Analysis of a nonlinear partial difference equation, and its application to cardiac dynamics. Zbl 1012.39004 Stubna, Michael D.; Rand, Richard H.; Gilmour, Robert F. jun.	7	2002
Nonlinear normal modes in a system with nonholonomic constraints. Zbl 1004.70009 Rand, R. H.; Ramani, D. V.	2	2001
Non-linear modal interactions in the oscillations of a liquid drop in a gravitational field. Zbl 1345.76035 Rozhkov, I.; Vakakis, A. F.; Rand, R. H.	1	2001
Sequences of orbits and the boundaries of the basin of attraction for two double heteroclinic orbits. Zbl 1068.70529 Haberman, Richard; Rand, Richard	1	2000
Resonant capture and separatrix crossing in dual-spin spacecraft. Zbl 0941.70021 Haberman, Richard; Rand, Richard; Yuster, Thomas	3	1999
Transition curves for the quasi-periodic Mathieu equation. Zbl 0916.34031 Zounes, Randolph S.; Rand, Richard H.	30	1998
How to pump a swing. Zbl 0995.70502 Wirkus, Stephen; Rand, Richard; Ruina, Andy	8	1998
Modal analysis of a cracked beam. Zbl 1235.74056 Chati, M.; Rand, R.; Mukherjee, S.	16	1997
Relaxation oscillations in tidally evolving satellites. Zbl 0922.70018 Quinn, Dane; Gladman, Brett; Nicholson, Phil; Rand, Richard	1	1997
Nonlinear control of dual-spin spacecraft during despin through precession phase lock. Zbl 0855.93057 Kinsey, R. J.; Mingori, D. L.; Rand, R. H.	5	1996
Dynamics of a nonlinear parametrically-excited PDE: 2-term truncation. Zbl 0868.35007 Rand, Richard H.	2	1996
A quasiperiodic Mathieu equation. Zbl 0918.34033 Rand, Richard; Zounes, Randolph; Hastings, Rachel	6	1995
Resonant capture in a system of two coupled homoclinic oscillators. Zbl 0949.34506 Rand, R. H.; Quinn, D. D.	4	1995
Topics in nonlinear dynamics with computer algebra. Zbl 0853.70001 Rand, Richard H.	10	1994
Oscillatory reaction-diffusion equations on rings. Zbl 0802.92002 Lubkin, Sharon; Rand, Richard	4	1994
Perturbation methods and computer algebra in mechanics. Zbl 0828.73080 Rand, R. H.	3	1994
Dynamics of spinup through resonance. Zbl 0825.70085 Rand, R. H.; Kinsey, R. J.; Mingori, D. L.	14	1992
Normal modes and global dynamics of a two-degree-of-freedom non-linear system. I: Low energies. Zbl 0765.70014 Vakakis, A. F.; Rand, R. H.	13	1992
Normal modes and global dynamics of a two-degree-of-freedom non-linear system. II: High energies. Zbl 0765.70015 Vakakis, A. F.; Rand, R. H.	7	1992
Bifurcation of nonlinear normal modes in a class of two degree of freedom systems. Zbl 0793.70014 Rand, R. H.; Pak, C. H.; Vakakis, A. F.	5	1992
MACSYMA program to implement averging using elliptic functions. Zbl 0741.65055 Coppola, Vincent T.; Rand, Richard H.	3	1991
Averaging using elliptic functions: Approximation of limit cycles. Zbl 0699.34032 Coppola, V. T.; Rand, R. H.	31	1990
Integrability of plane quadratic vector fields. Zbl 0693.34030 Schlomiuk, Dana; Guckenheimer, John; Rand, Richard	23	1990
Bifurcations and chaos in a forced zero-stiffness impact oscillator. Zbl 0714.73049 Li, G. X.; Rand, R. H.; Moon, F. C.	15	1990
The transition to chaos in a simple mechanical system. Zbl 0666.70030 Shaw, Steven W.; Rand, Richard H.	40	1989
Analytical approximation for period-doubling following a Hopf bifurcation. Zbl 0684.58030 Rand, Richard H.	12	1989
Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems. Zbl 0677.58038 Guckenheimer, John; Rand, Richard; Schlomiuk, Dana	10	1989
Computer algebra implementation of Lie transforms for Hamiltonian systems: Application to the nonlinear stability of \(L_ 4\). Zbl 0696.70015 Coppola, V. T.; Rand, R. H.	3	1989
Resonance in a high-speed flexible-arm robot. Zbl 0681.70028 Golnaraghi, M. F.; Moon, F. C.; Rand, R. H.	1	1989
Symbolic computation and perturbation methods using elliptic functions. Zbl 0689.33002 Coppola, Vincent T.; Rand, Richard H.	1	1989
The transition from phase locking to drift in a system of two weakly coupled Van Der Pol oscillators. Zbl 0667.70028 Chakraborty, Tapesh; Rand, Richard H.	27	1988
Lie transforms applied to a nonlinear parametric excitation problem. Zbl 0655.70020 Len, Jonathan L.; Rand, Richard H.	1	1988
Perturbation methods, bifurcation theory and computer algebra. Zbl 0651.34001 Rand, Richard H.; Armbruster, Dieter	67	1987
A simplified model of coupled relaxation oscillators. Zbl 0614.73024 Storti, Duane; Rand, Richard H.	9	1987
Determinacy of degenerate equilibria with linear part \(x'=y\), \(y'=0\) using MACSYMA. Zbl 0624.65068 Rand, R. H.; Keith, W. L.	4	1987
Dynamics of two strongly coupled relaxation oscillators. Zbl 0589.34043 Storti, D. W.; Rand, R. H.	10	1986
Some mathematical questions in biology. Plant biology. (Proceedings of the 1985 Symposium Some Mathematical Questions in Biology, held at the Annual Meeting of the American Association for the Advancement of Science in Los Angeles, California, May 27, 1985). Zbl 0604.92002	1	1986
Dynamics of a system exhibiting the global bifurcation of a limit cycle at infinity. Zbl 0647.34033 Keith, W. L.; Rand, R. H.	7	1985
Computer algebra in applied mathematics: an introduction to MACSYMA. Zbl 0583.68012 Rand, R. H.	38	1984
1:1 and 2:1 phase entrainment in a system of two coupled limit cycle oscillators. Zbl 0547.92001 Keith, W. L.; Rand, R. H.	5	1984
Fluid mechanics of green plants. Zbl 0564.76128 Rand, Richard H.	2	1983
...and 19 more Documents

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Cited by 1,337 Authors

46	Rand, Richard H.
18	Belhaq, Mohamed
17	Luo, Albert C. J.
14	Pender, Jamol J.
10	Llibre, Jaume
9	Gendelman, Oleg V.
9	Xu, Jian
8	Tkhaĭ, Valentin Nikolaevich
8	Vakakis, Alexander F.
7	Bi, Qinsheng
7	Verdugo, Anael
7	Xu, Wei
7	Zhang, Tonghua
6	Du, Zhengdong
6	Lakrad, Faouzi
6	Rashidi, Mohammad Mehdi
6	Yu, Pei
5	Chen, Yushu
5	Ermentrout, George Bard
5	Kuznetsov, Aleksandr Petrovich
5	Porter, Mason Alexander
5	Quinn, D. Dane
5	Sah, Si Mohamed
5	Song, Yongli
5	Strogatz, Steven Henry
5	Wesson, Elizabeth N.
4	Abouhazim, Nazha
4	Balthazar, José Manoel
4	Bergman, Lawrence A.
4	Caldas, Iberê L.
4	Chatterjee, Anindya
4	Chung, Kwok-Wai
4	de Wolff, Babette A. J.
4	Dinarvand, Saeed
4	Doldo, Philip
4	Elías-Zúñiga, Alex
4	Fahsi, Abdelhak
4	Holmes, Philip J.
4	Hu, Wenjun
4	Kiemel, Tim
4	Kopell, Nancy J.
4	Kovacic, Ivana
4	Lenci, Stefano
4	Leung, Andrew Yee-Tak
4	Liu, Yirong
4	Rega, Giuseppe
4	Rezazadeh, Ghader
4	Schlomiuk, Dana I.
4	Sun, Zhongkui
4	Turukina, Ludmila V.
4	Valls Anglés, Cláudia
4	Wang, Zaihua
4	Wirkus, Stephen A.
4	Younesian, Davood
4	Zhang, Gang
4	Zhang, Weinian
3	Barabanov, Ivan N.
3	Bhattacharjee, Jayanta K.
3	Bridge, Jacqueline
3	Camacho, Erika T.
3	Chabi Orou, Jean B.
3	Collins, James J.
3	Coombes, Stephen
3	Corless, Robert Malcolm
3	Dankowicz, Harry J.
3	de Souza, Silvio Luiz Thomaz
3	Doroshin, Anton V.
3	Golnaraghi, M. Farid
3	Guo, Chuan
3	Hacinliyan, Avadis Simon
3	Hamdi, Mustapha
3	Hoffman, Kathleen A.
3	Ishibashi, Kazuki
3	Kelso, J. A. Scott
3	Li, Jibin
3	Li, Yurong
3	Lu, Qishao
3	Luongo, Angelo
3	Moiola, Jorge Luis
3	Osipov, Grigory V.
3	Rand, David G.
3	Roberts, Anthony John
3	Salas, Alvaro H.
3	Schneider, Isabelle
3	Sheheitli, Hiba
3	Siddiqui, Abdul Majeed
3	Stewart, Ian Nicholas
3	Tian, Haiyan
3	Tschauner, Johann
3	Vestroni, Fabrizio
3	Wahi, Pankaj
3	Wu, Zhiqiang
3	Yang, Xiaoli
3	Zang, Hong
2	Alharthi, Muteb R.
2	Alvarez, Edgardo
2	Aronson, Donald G.
2	Avramov, Konstantin V.
2	Aybar, Orhan Ozgur
2	Azizi, Saber
...and 1,237 more Authors

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Cited in 194 Serials

99	Nonlinear Dynamics
59	Communications in Nonlinear Science and Numerical Simulation
52	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
46	Physica D
33	Chaos, Solitons and Fractals
29	Chaos
19	Applied Mathematics and Computation
13	Journal of Mathematical Biology
13	Meccanica
12	Biological Cybernetics
11	Applied Mathematics and Mechanics. (English Edition)
10	Physica A
10	Applied Mathematical Modelling
10	Nonlinear Analysis. Real World Applications
10	Journal of Theoretical Biology
9	Mathematical Problems in Engineering
9	Journal of Vibration and Control
8	Journal of Applied Nonlinear Dynamics
7	Celestial Mechanics
7	SIAM Journal on Applied Dynamical Systems
6	Journal of Mathematical Analysis and Applications
6	Physics of Fluids
6	Automation and Remote Control
5	Acta Mechanica
5	Physics Letters. A
5	Bulletin of Mathematical Biology
5	Journal of Computational and Applied Mathematics
5	Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
5	Journal of Symbolic Computation
5	Queueing Systems
5	Journal of Nonlinear Science
4	Computers & Mathematics with Applications
4	Journal of Mathematical Physics
4	Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
4	Automatica
4	Journal of Differential Equations
4	Dynamics and Stability of Systems
4	Journal of Computer and Systems Sciences International
4	Qualitative Theory of Dynamical Systems
3	Computer Methods in Applied Mechanics and Engineering
3	International Journal of Control
3	International Journal of Engineering Science
3	Journal of Applied Mathematics and Mechanics
3	Journal of Computational Physics
3	Journal of Statistical Physics
3	Mathematical Biosciences
3	Computational Mechanics
3	European Journal of Operational Research
3	Archive of Applied Mechanics
3	Complexity
3	International Journal of Structural Stability and Dynamics
3	Dynamic Games and Applications
3	Nonlinear Analysis. Theory, Methods & Applications
3	Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
3	Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
2	Artificial Intelligence
2	Computer Physics Communications
2	Journal of Fluid Mechanics
2	Journal of the Franklin Institute
2	Mathematical Methods in the Applied Sciences
2	ZAMP. Zeitschrift für angewandte Mathematik und Physik
2	Advances in Mathematics
2	International Journal for Numerical Methods in Engineering
2	Mathematics and Computers in Simulation
2	Mathematics of Operations Research
2	Operations Research
2	Insurance Mathematics & Economics
2	Applied Numerical Mathematics
2	Numerical Methods for Partial Differential Equations
2	Japan Journal of Industrial and Applied Mathematics
2	Computational Mathematics and Mathematical Physics
2	SIAM Journal on Applied Mathematics
2	Acta Mechanica Sinica. (English Edition)
2	Celestial Mechanics and Dynamical Astronomy
2	Continuum Mechanics and Thermodynamics
2	Computational and Applied Mathematics
2	NoDEA. Nonlinear Differential Equations and Applications
2	Journal of Computational Neuroscience
2	Discrete and Continuous Dynamical Systems
2	European Journal of Control
2	Abstract and Applied Analysis
2	Acta Mathematica Sinica. English Series
2	International Journal of Nonlinear Sciences and Numerical Simulation
2	Discrete and Continuous Dynamical Systems. Series B
2	Journal of Applied Mathematics
2	Advances in Difference Equations
2	European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
2	Acta Mechanica Sinica
2	Journal of Physics A: Mathematical and Theoretical
2	International Journal of Biomathematics
2	Communications in Theoretical Physics
2	Advances in Mathematical Physics
2	Advances in Applied Mathematics and Mechanics
2	Science China. Technological Sciences
2	Asian Journal of Control
2	Afrika Matematika
2	The Journal of Mathematical Neuroscience
2	Stochastic Systems
2	Discontinuity, Nonlinearity, and Complexity
1	Advances in Applied Probability
...and 94 more Serials

all top 5

Cited in 41 Fields

381	Ordinary differential equations (34-XX)
219	Mechanics of particles and systems (70-XX)
173	Dynamical systems and ergodic theory (37-XX)
121	Biology and other natural sciences (92-XX)
84	Systems theory; control (93-XX)
63	Mechanics of deformable solids (74-XX)
51	Numerical analysis (65-XX)
40	Computer science (68-XX)
35	Partial differential equations (35-XX)
35	Fluid mechanics (76-XX)
25	Probability theory and stochastic processes (60-XX)
25	Game theory, economics, finance, and other social and behavioral sciences (91-XX)
24	Operations research, mathematical programming (90-XX)
18	Statistical mechanics, structure of matter (82-XX)
9	Optics, electromagnetic theory (78-XX)
7	Classical thermodynamics, heat transfer (80-XX)
6	Difference and functional equations (39-XX)
6	Quantum theory (81-XX)
6	Information and communication theory, circuits (94-XX)
5	Harmonic analysis on Euclidean spaces (42-XX)
5	Operator theory (47-XX)
4	Real functions (26-XX)
4	Statistics (62-XX)
3	History and biography (01-XX)
3	Combinatorics (05-XX)
3	Calculus of variations and optimal control; optimization (49-XX)
2	General and overarching topics; collections (00-XX)
2	Approximations and expansions (41-XX)
2	Integral equations (45-XX)
2	Global analysis, analysis on manifolds (58-XX)
1	Field theory and polynomials (12-XX)
1	Commutative algebra (13-XX)
1	Algebraic geometry (14-XX)
1	Linear and multilinear algebra; matrix theory (15-XX)
1	Topological groups, Lie groups (22-XX)
1	Measure and integration (28-XX)
1	Potential theory (31-XX)
1	Special functions (33-XX)
1	Sequences, series, summability (40-XX)
1	Functional analysis (46-XX)
1	Relativity and gravitational theory (83-XX)

Rand, Richard H.

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Cited by 1,337 Authors

Cited in 194 Serials

Cited in 41 Fields

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