| [1] |
Steven, S.; Mark, F., Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Comput Phys, 8, 5, 532 (1994) |
| [2] |
Zhou, S.; Lin, X.; Hua, L., Chaotic synchronization of a fractional-order system based on washout filter control, Commun Nonlinear Sci Numer Simul, 16, 3, 1533-1540 (2011) |
| [3] |
Namayanja, P., Chaotic dynamics in a transport equation on a network, Discrete Contin Dynam Syst, 23, 8, 3415-3426 (2018) · Zbl 1475.34034 |
| [4] |
Gyllenberg, M.; Jiang, J.; Niu, L., Chaotic attractors in the four-dimensional Leslie-Gower competition model, Physica D, 402, 15, Article 132186 pp. (2019) · Zbl 1453.37084 |
| [5] |
Lundstrom, B. N.; Higgs, M. H.; Spain, W. J.; Fairhall, A. L., Fractional differentiation by neocortical pyramidal neurons, Nat Neurosci, 11, 11, 1335-1342 (2008) |
| [6] |
Li, C. L.; Mei, Z.; Feng, Z.; Yang, X. B., Projective synchronization for a fractional-order chaotic system via single sinusoidal coupling, Optik, 127, 5, 2830-2836 (2016) |
| [7] |
Zhou, S.; Lan, X.; Yang, X., A sufficient condition for the existence of a k-factor excluding a given r-factor, Appl Math Nonlinear Sci, 2, 1, 13-20 (2017) · Zbl 1375.05222 |
| [8] |
Gao, Q.; Ma, J., Chaos and hopf bifurcation of a finance system, Nonlinear Dyn, 58, 1, 209 (2009) · Zbl 1183.91193 |
| [9] |
Mircea, G.; Neamu, M.; Bundu, O.; Opri, D., Uncertain and stochastic financial models with multiple delays, Int J Bifurcation Chaos, 22, 6, 19 (2012) · Zbl 1270.34190 |
| [10] |
Chian, C. L., Nonlinear dynamics and chaos in macroeconomics, Int J Theor Appl Finan, 3, 3, 601 (2000) |
| [11] |
Lorenz, H. W., Nonlinear dynamical economics and chaotic motion (1993), Springer: Springer Berlin, Heidelberg · Zbl 0841.90036 |
| [12] |
Panas, E., Long memory and chaotic models of prices on the London metal exchange, Resour Policy, 27, 4, 235-246 (2001) |
| [13] |
Bruce, J.; West, Sergio; Picozzi, Fractional Langevin model of memory in financial time series, Physical Review E, 65, 3 (2002), 37106-37106 |
| [14] |
Meyers, Robert A., Complex systems in finance and econometrics (2011), Springer: Springer New York · Zbl 1350.91009 |
| [15] |
Klioutchnikov, I.; Sigova, M.; Beizerov, N., Chaos theory in finance, Procedia Comput Sci, 119, 1, 368-375 (2017) |
| [16] |
Ma, J. H.; Chen, Y. S., Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (I), Appl Math Mech, 22, 11, 1240-1251 (2001) · Zbl 1001.91501 |
| [17] |
Ma, J. H.; Chen, Y. S., Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (II), Appl Math Mech, 22, 12, 1375-1382 (2001) · Zbl 1143.91341 |
| [18] |
Li, L. S., Synchronization of a chaotic finance system, Appl Math Comput, 217, 13, 6031-6039 (2011) · Zbl 1208.91175 |
| [19] |
Pan, I.; Das, S., Multi-objective active control policy design for commensurate and incommensurate fractional order chaotic financial systems, App Math Model, 39, 2, 500-514 (2015) · Zbl 1432.91113 |
| [20] |
Wu, C. F.; Chen, B. S.; Zhang, W., Multiobjective investment policy for nonlinear stochastic financial system: fuzzy approach, IEEE Trans Fuzzy Syst, 25, 2, 460-474 (2016) |
| [21] |
Abd-Elouabhab, M. S.; Hamri, N. E.; Wang, J., Chaos control of a fractional-order financial system, Math Probl Eng, 2010, Article 270646 pp. (2010) · Zbl 1195.91185 |
| [22] |
Yang, T., Dynamical analysis on a finance system with nonconstant elasticity of demand, Int J Bifurcation Chaos, 30, 10, 2050148 (2020) · Zbl 1451.37117 |
| [23] |
Hajipour, A.; Hajipour, M.; Baleanu, D., On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system, Physica A, 15, 2, 1-3 (2018) |
| [24] |
Riahi, A.; Noghredani, N.; Shajiee, M.; Pariz, N., Synchronization of a novel class of fractional-order uncertain chaotic systems via adaptive sliding mode controller, Int J Control Autom, 9, 1, 63-80 (2016) |
| [25] |
Bhalekar, S.; Daftardar-Gejji, V., Synchronization of different fractional order chaotic systems using active control, Commun Nonlinear Sci Numer Simul, 15, 11, 3536-3546 (2010) · Zbl 1222.94031 |
| [26] |
Danca, M. F.; Garrappa, R., Suppressing chaos in discontinuous systems of fractional order by active control, Chaotic Dyn, 257, 1, 89-102 (2014) · Zbl 1338.34112 |
| [27] |
Srivastava, M.; Ansari, S. P.; Agrawal, S. K.; Das, S.; Leung, A., Anti-synchronization between identical and non-identical fractional-order chaotic systems using active control method, Nonlinear Dyn, 76, 2, 905-914 (2013) |
| [28] |
Agrawal, S. K.; Srivastava, M.; Da, S. S., Synchronization of fractional order chaotic systems using active control method, Chaos Solitons Fractals, 45, 6, 737-752 (2012) |
| [29] |
Atangana, A.; Baleanu, D., New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model, Therm Sci, 20, 2, 763-769 (2016) |
| [30] |
Atangana, A.; Gómez-Aguilar, J., Decolonisation of fractional calculus rules: breaking commutativity and associativity to capture more natural phenomena, Eur Phys J Plus, 133, 4, 166 (2018) |
| [31] |
Atangana, A.; Koca, I., Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order, Chaos Solitons Fractals, 89, 1, 447-454 (2016) · Zbl 1360.34150 |
| [32] |
Lin, X.; Wang, Y.; Wu, G.; Hao, J., Image denoising of adaptive fractional operator based on Atangana-Baleanu derivatives, J Math, 2021, 3, 1-16 (2021) · Zbl 1477.94017 |
| [33] |
Alkahtani, B., Chua’s circuit model with Atangana-Baleanu derivative with fractional order, Chaos Solitons Fractals, 89, 1, 547-551 (2016) · Zbl 1360.34160 |
| [34] |
Antonio, M.; Deeónab, C., Stability and Lyapunov functions for systems with Atangana-Baleanu Caputo derivative: an HIV/AIDS epidemic model, Chaos Solitons Fractals, 132, 1, Article 109586 pp. (2020) · Zbl 1434.92020 |
| [35] |
Gottwald, G. A.; Melbourne, I., Testing for chaos in deterministic systems with noise, Physica D, 212, 1-2, 100-110 (2005) · Zbl 1097.37024 |
| [36] |
Gottwald, G. A.; Melbourne, I., On the implementation of the 0-1 test for chaos, Chaotic Dyn, 8, 1, 129-145 (2009) · Zbl 1161.37054 |
| [37] |
Matignon, D., Stability results for fractional differential equations with applications to control processing, Comput Eng Syst Appl, 2, 963-968 (1996) |
| [38] |
Thabet, A., A lyapunov type inequality for fractional operators with nonsingular Mittag-Leffler kernel, Journal of Inequalities and Applications, 1, 130 (2017) · Zbl 1368.26003 |
| [39] |
Guo, R., Projective synchronization of a class of chaotic systems by dynamic feedback control method, Nonlinear Dyn, 90, 53-64 (2017) · Zbl 1390.34168 |
| [40] |
Liu, H.; Li, S.; Sun, Y.; Wang, H., Adaptive fuzzy synchronization for uncertain fractional-order chaotic systems with unknown non-symmetrical control gain, Acta Phys Sin, 070503 (2015) |
