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Dynamics of synchronous Boolean networks with non-binary states. (English) Zbl 07901224

MSC:

37-XX Dynamical systems and ergodic theory
34-XX Ordinary differential equations

References:

[1] Adiga, A.; Kuhlman, C. J.; Marathe, M. V.; Mortveit, H. S.; Ravi, S. S.; Vullikanti, A., Graphical dynamical systems and their applications to bio-social systems, Int. J. Adv. Eng. Sci. Appl. Math., 11, 153-171, 2019 · doi:10.1007/s12572-018-0237-6
[2] Deshpande, A.; Samanta, S.; Govindarajan, S.; Layek, R. K., Multi-bit Boolean model for chemotactic drift of Escherichia coli, IET Syst. Biol., 14, 343-349, 2020 · doi:10.1049/iet-syb.2020.0060
[3] Deutsch, A.; Dormann, S., Cellular Automaton Modelling of Biological Pattern Formation, 2004, Birkhäuser: Birkhäuser, Boston, MA
[4] Robeva, R. S., Algebraic and Discrete Mathematical Methods for Modern Biology, 2015, Academic Press · Zbl 1314.92017
[5] Siebert, H., Analysis of discrete bioregulatory networks using symbolic steady states, Bull Math. Biol., 73, 873-898, 2011 · Zbl 1214.92033 · doi:10.1007/s11538-010-9609-1
[6] Sole, R. V.; Luque, B.; Kauffman, S.
[7] Toroczkai, Z.; Guclu, H., Proximity networks and epidemics, Physica A, 378, 68, 2007 · doi:10.1016/j.physa.2006.11.088
[8] Laubenbacher, R.; Stigler, B., A computational algebra approach to the reverse engineering of gene regulatory networks, J. Theor. Biol., 229, 523-537, 2004 · Zbl 1440.92032 · doi:10.1016/j.jtbi.2004.04.037
[9] Shmulevich, I.; Dougherty, E. R., Probabilistic Boolean Networks: The Modeling and Control of Gene Regulatory Networks, 2010, SIAM · Zbl 1320.92020
[10] Shmulevich, I.; Dougherty, E. R.; Zhang, W., From Boolean to probabilistic Boolean networks as models of genetic regulatory networks, Proc. IEEE, 90, 1778-1792, 2002 · doi:10.1109/JPROC.2002.804686
[11] Cardell, S. D.; Fuster-Sabater, A., Binomial representation of cryptographic binary sequences and its relation to cellular automata, Complexity, 2019, 2108014, 2019 · Zbl 1421.94029 · doi:10.1155/2019/2108014
[12] Fuster-Sabater, A.; Caballero-Gil, P., On the use of cellular automata in symmetric cryptography, Acta Appl. Math., 93, 215-236, 2006 · Zbl 1151.94011 · doi:10.1007/s10440-006-9041-6
[13] Cattaneo, G.; Comito, M.; Bianucci, D., Sand piles: From physics to cellular automata models, Theor. Comput. Sci., 436, 35-53, 2012 · Zbl 1251.37017 · doi:10.1016/j.tcs.2012.02.034
[14] Chopard, B.; Droz, M., Cellular Automata Modeling of Physical Systems, 1998, Cambridge University Press: Cambridge University Press, Cambridge · Zbl 0973.82033
[15] Jian, F.; Danddan, S., Complex network theory and its applications research on P2P networks, Appl. Math. Nonlinear Sci., 1, 45-52, 2016 · Zbl 1423.68052 · doi:10.21042/AMNS.2016.1.00004
[16] Cattaneo, G.; Chiaselotti, G.; Dennunzio, A.; Formenti, E.; Manzoni, L., Non uniform cellular automata description of signed partition versions of ice and sand pile models, Proc. Cell. Autom. ACRI Lect. Not. Comput. Sci., 8751, 115-124, 2014 · doi:10.1007/978-3-319-11520-7_13
[17] Cattaneo, G.; Chiaselotti, G.; Oliverio, P. A.; Stumbo, F., A new discrete dynamical system of signed integer partitions, Eur. J. Comb., 55, 119-143, 2016 · Zbl 1333.05026 · doi:10.1016/j.ejc.2016.02.003
[18] Chiaselotti, G.; Gentile, T.; Oliverio, P. A., Parallel and sequential dynamics of two discrete models of signed integer partitions, Appl. Math. Comput., 232, 1249-1261, 2014 · Zbl 1410.37015 · doi:10.1016/j.amc.2014.01.118
[19] Hofbauer, J.; Sigmund, K., Evolutionary Games and Population Dynamics, 2003, Cambridge University Press: Cambridge University Press, Cambridge
[20] Kawachi, A.; Ogihara, M.; Uchizawa, K., Generalized predecessor existence problems for Boolean finite dynamical systems on directed graphs, Theor. Comput. Sci., 762, 25-40, 2019 · Zbl 1434.68315 · doi:10.1016/j.tcs.2018.08.026
[21] Ogihara, M.; Uchizawa, K., Synchronous Boolean finite dynamical systems on directed graphs over XOR functions, Theory Comput. Syst., 67, 569-591, 2023 · Zbl 07719398 · doi:10.1007/s00224-022-10111-x
[22] Siegel, P.; Doncescu, A.; Risch, V.; Sené, S., Representation of gene regulation networks by hypothesis logic-based Boolean systems, J. Supercomput., 79, 4556-4581, 2023 · doi:10.1007/s11227-022-04809-5
[23] Aledo, J. A.; Martinez, S.; Valverde, J. C., Parallel dynamical systems over graphs and related topics: A survey, J. Appl. Math., 2015, 594294, 2015 · Zbl 1435.37024 · doi:10.1155/2015/594294
[24] Barrett, C. L.; Chen, W. Y. C.; Zheng, M. J., Discrete dynamical systems on graphs and Boolean functions, Math. Comput. Simul., 66, 487-497, 2004 · Zbl 1113.37005 · doi:10.1016/j.matcom.2004.03.003
[25] Gershenson, C.
[26] Mortveit, H. S.; Reidys, C. M., An Introduction to Sequential Dynamical Systems, 2007, Springer: Springer, New York
[27] Aledo, J. A.; Barzanouni, A.; Malekbala, G.; Sharifan, L.; Valverde, J. C., On the periodic structure of parallel dynamical systems on generalized independent Boolean functions, Mathematics, 8, 1088, 2020 · doi:10.3390/math8071088
[28] Aledo, J. A.; Martinez, S.; Valverde, J. C., Parallel discrete dynamical systems on independent local functions, J. Comput. Appl. Math., 237, 335-339, 2013 · Zbl 1248.37077 · doi:10.1016/j.cam.2012.06.002
[29] Chen, R. X. F.; McNitt, J. A.; Mortveit, H. S.; Pederson, R. D.; Reidys, C. M., Lipschitz continuity under toric equivalence for asynchronous Boolean networks, Chaos, 33, 023118, 2023 · Zbl 07881245 · doi:10.1063/5.0119621
[30] Aledo, J. A.; Martinez, S.; Pelayo, F. L.; Valverde, J. C., Parallel dynamical systems on maxterm and minterm Boolean functions, Math. Comput. Model., 55, 666-671, 2012 · Zbl 1255.37003 · doi:10.1016/j.mcm.2011.08.040
[31] Aledo, J. A.; Martinez, S.; Valverde, J. C., Parallel dynamical systems over directed dependency graphs, Appl. Math. Comput., 219, 1114-1119, 2012 · Zbl 1291.37018 · doi:10.1016/j.amc.2012.07.018
[32] Aledo, J. A.; Diaz, L. G.; Martinez, S.; Valverde, J. C., On the periods of parallel dynamical systems, Complexity, 2017, 7209762, 2017 · Zbl 1367.94485 · doi:10.1155/2017/7209762
[33] Aledo, J. A.; Diaz, L. G.; Martinez, S.; Valverde, J. C., Coexistence of periods in parallel and sequential Boolean graph dynamical systems over directed graphs, Mathematics, 8, 1812, 2020 · doi:10.3390/math8101812
[34] Aledo, J. A.; Diaz, L. G.; Martinez, S.; Valverde, J. C., Maximum number of periodic orbits in parallel dynamical systems, Inf. Sci., 468, 63-71, 2018 · Zbl 1451.37027 · doi:10.1016/j.ins.2018.08.041
[35] Aledo, J. A.; Barzanouni, A.; Malekbala, G.; Sharifan, L.; Valverde, J. C., Counting periodic points in parallel graph dynamical systems, Complexity, 2020, 9708347 · Zbl 1455.37038 · doi:10.1155/2020/9708347
[36] Aledo, J. A.; Martinez, S.; Valverde, J. C., Updating method for the computation of orbits in parallel and sequential dynamical systems, Int. J. Comput. Math., 90, 1796-1808, 2013 · Zbl 1354.37045 · doi:10.1080/00207160.2013.767894
[37] Aledo, J. A.; Diaz, L. G.; Martinez, S.; Valverde, J. C., Predecessors and garden-of-eden configurations in parallel dynamical systems on maxterm and minterm Boolean functions, J. Comput. Appl. Math., 348, 26-33, 2019 · Zbl 1404.37043 · doi:10.1016/j.cam.2018.08.015
[38] Aledo, J. A.; Diaz, L. G.; Martinez, S.; Valverde, J. C., Dynamical attraction in parallel network models, Appl. Math. Comput., 361, 874-888, 2019 · Zbl 1428.90030 · doi:10.1016/j.amc.2019.05.048
[39] Luque, B.; Ballesteros, F. J., Random walk networks, Physica A, 342, 207-213, 2004 · doi:10.1016/j.physa.2004.04.080
[40] Zou, Y. M., Boolean networks with multiexpressions and parameters, IEEE/ACM Trans. Comput. Biol. Bioinf., 10, 584-592, 2013 · doi:10.1109/TCBB.2013.79
[41] Aledo, J. A.; Martinez, S.; Valverde, J. C., Graph dynamical systems with general Boolean states, 9, 1803-1808, 2015
[42] Stone, M. H., The theory of representations for Boolean algebras, Trans. Am. Math. Soc., 40, 37-111, 1936 · JFM 62.0033.04 · doi:10.1090/S0002-9947-1936-1501865-8
[43] Aledo, J. A.; Barzanouni, A.; Malekbala, G.; Sharifan, L.; Valverde, J. C., Fixed points in generalized parallel and sequential dynamical systems induced by a minterm or maxterm Boolean functions, J. Comput. Appl. Math., 408, 114070, 2022 · Zbl 1484.94036 · doi:10.1016/j.cam.2021.114070
[44] Aledo, J. A.; Goles, E.; Montalva-Medel, M.; Montealegre, P.; Valverde, J. C., Symmetrizable Boolean networks, Inf. Sci., 626, 787-804, 2023 · Zbl 1541.94092 · doi:10.1016/j.ins.2023.01.082
[45] Rosen, K., Discrete Mathematics and Its Applications, 2019, McGraw-Hill Education
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