zbMATH — the first resource for mathematics

Collective behavior of a nearest neighbor coupled system in a dichotomous fluctuating potential. (English) Zbl 07274902
Summary: In this study, the collective and stochastic resonance (SR) behavior of a stochastic nearest neighbor coupled system in a dichotomous fluctuating potential driven by a periodic force are investigated. The exact conditions of stability, synchronization and SR of the system are given analytically and verified by a numerical algorithm. We find that the final dynamic behaviors of the system are the results of the synergy of the coupled system, noise and external periodic force: the stationary regime criterion is only related to the noise parameters and system potential parameter; the synchronization criterion is related to the number of particles, coupling strength, noise parameters and system potential parameter. Furthermore, for the stationary regime, all particles synchronously move with their mean field and show SR phenomenon. For the non-stationary regime, the power-law distribution is observed when the synchronization criteria is satisfied.
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
Full Text: DOI
[1] Bar-Yam, Y., Dynamics of complex systems (1997), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 1074.37041
[2] He, W.; Cao, J., Exponential synchronization of hybrid coupled networks with delayed coupling, IEEE Trans Neural Netw, 21, 571-583 (2010)
[3] Li, L.; Xiao, J.; Peng, H., Improving synchronous ability between complex networks, Nonlinear Dyn, 69, 1105-1110 (2012)
[4] Zhang, L.; Harnefors, L.; Nee, H. P., Power-synchronization control of grid-connected voltage-source converters, IEEE Trans Power Syst, 25, 809-820 (2010)
[5] Tian, H. P.; . Wei, B., Stability control of flight attitude angle for four rotor aircraft, IEEE 9th International conference on software engineering and service science, 332-336 (2018)
[6] Zhen, Z. G., Emergence dynamics in complex systems: from synchronization to collective transport-i (in Chinese) (2019), Science Press: Science Press Beijing
[7] Pikovsky, A.; Rosenblum, M.; Kurths, J., Synchronization-a universal concept in nonlinear sciences (2001), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0993.37002
[8] Rulkov, N.; Sushchik, M.; Tsimring, L., Generalized synchronization of chaos in directionally coupled chaotic systems, Phys Rev E, 51, 980-994 (1995)
[9] Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J., From phase to lag synchronization in coupled chaotic oscillators, Phys Rev Lett, 78, 4193-4196 (1997)
[10] Erjaee, G. H.; Taghvafard, H., Stability analysis of phase synchronization in coupled chaotic systems presented by fractional differential equations, Nonlinear Dyn Syst Theory, 2, 332-337 (2011) · Zbl 1235.34152
[11] Goldobin, D. S.; Dolmatova, A. V., Interplay of the mechanisms of synchronization by common noise and global coupling for a general class of limit-cycle oscillators, Commun Nonlinear Sci Numer Simul, 75, 94-108 (2019) · Zbl 07264425
[12] Wang, C. J.; Long, F.; Zhang, P., Controlling of stochastic resonance and noise enhanced stability induced by harmonic noises in a bistable system, Physica A, 471, 288-294 (2017) · Zbl 1400.34099
[13] Lindner, J. F.; Meadows, B. K.; Ditto, W. L., Array enhanced stochastic resonance and spatiotemporal synchronization, Phys Rev Lett, 75, 3-6 (1995)
[14] Xiao, Y. Z.; Tang, S. F.; Sun, Z. K., The role of multiplicative noise in complete synchronization of bidirectionally coupled chain, Eur Phys J B, 87, 134-141 (2014)
[15] Gomez-Ordonez, J.; Casado, J. M.; Morillo, M., Arrays of noisy bistable elements with nearest neighbor coupling: equilibrium and stochastic resonance, Eur Phys J B, 82, 2, 179-187 (2011)
[16] Lindner, J. F.; Meadows, B. K.; Ditto, W. L., Scaling laws for spatiotemporal synchronization and array enhanced stochastic resonance, Phys Rev E, 53, 3, 2081-2086 (1996)
[17] Shi, J. C.; Luo, M.; Dong, T., The selectivity of noise and coupling for coherence biresonance and array-enhanced coherence biresonance in coupled neural systems, BioSystems, 98, 2, 85-90 (2009)
[18] Li, J. H., Effect of asymmetry on stochastic resonance and stochastic resonance induced by multiplicative noise and by mean-field coupling, Phys Rev E, 66, 031104 (2002)
[19] Lin, L. F.; Wang, H. Q., Tempered Mittag-Leffler noise-induced resonant behaviors in the generalized Langevin system with random mass, Nonlinear Dyn, 98, 801-817 (2019)
[20] Gitterman, M., Classical harmonic oscillator with multiplicative noise, Physica A, 352, 309-334 (2005)
[21] Van Den Broeck, C., On the relation between white shot noise, gaussian white noise, and the dichotomic Markov process, J Stat Phys, 31, 467-483 (1983) · Zbl 0588.60081
[22] Gitterman, M., Harmonic oscillator with multiplicative noise: nonmonotonic dependence on the strength and the rate of dichotomous noise, Phys Rev E, 67, 057103 (2003)
[23] Zhang, L.; Zhong, S. C.; Peng, H., Stochastic multi-resonance in a linear system driven by multiplicative polynomial dichotomous noise, Chin Phys Lett, 28, 090505 (2011)
[24] Yu, T.; Zhang, L.; Zhong, S. C., The resonance behavior in two coupled harmonic oscillators with fluctuating mass, Nonlinear Dyn, 96, 1735-1745 (2019) · Zbl 1437.70032
[25] Yu, T.; Zhang, L.; Ji, Y. D., Stochastic resonance of two coupled fractional harmonic oscillators with fluctuating mass, Commun Nonlinear Sci Numer Simul, 72, 26-38 (2019) · Zbl 07264727
[26] Yang, B.; Zhang, X.; Zhang, L., Collective behavior of globally coupled Langevin equations with colored noise in the presence of stochastic resonance, Phys Rev E, 94, 022119 (2016)
[27] Lai, L.; Zhang, L.; Yu, T., Collective behaviors in globally coupled harmonic oscillators with fluctuating damping coefficient, Nonlinear Dyn, 97, 2231-2248 (2019) · Zbl 1430.34045
[28] Sornette, D., Probability distributions in complex systems, Computational complexity (2012), Springer: Springer New York
[29] Barabasi, A.; Albert, R., Emergence of scaling in random networks, Science, 286, 509-512 (1999) · Zbl 1226.05223
[30] Saul, I. G.; Harris, C. M., Encyclopedia of operations research and management science (1996), Springer: Springer New York · Zbl 0863.90110
[31] Berdichevsky, V.; . Gitterman, M., Multiplicative stochastic resonance in linear systems: analytical solution, Europhys Lett, 36, 161-166 (1996) · Zbl 0907.58060
[32] Zhang, L.; Lai, L.; Peng, H., Stochastic and superharmonic stochastic resonances of a confined overdamped harmonic oscillator, Phys Rev E, 97, 012147 (2018)
[33] Fulinski, A., Changes in transition rates due to barrier fluctuations: the case of dichotomic noise, Phys Lett A, 180, 94-98 (1993)
[34] Robertson, B.; Astumian, R. D., Frequency dependence of catalyzed reactions in a weak oscillating field, J Chem Phys, 94, 7414-7418 (1991)
[35] Hasty, J.; Pradines, J.; Dolnik, M., Noise-based switches and amplifiers for gene expression, PNAS, 97, 2075-2080 (2000)
[36] Kubo, R., Stochastic Liouville equations, J Math Phys, 4, 174-183 (1963) · Zbl 0135.45102
[37] Scott, A., Neuroscience: a mathematical primer (2002), Springer: Springer New York · Zbl 1018.92003
[38] Li, J. H.; Chen, Q. H.; Zhou, X. F., Transport and its enhancement caused by coupling, Phys Rev E, 81, 041104 (2010)
[39] Lv, J. P.; Liu, H.; Chen, Q. H., Phase transition in site-diluted Josephson junction arrays: a numerical study, Phys Rev B, 79, 104512 (2009)
[40] Wang, Q. Y.; Perc, M.; Duan, Z. S.; Chen, G. R., Delay-induced multiple stochastic resonances on scale-free neuronal networks, Chaos, 19, 023112 (2009)
[41] Marchesoni, F., Thermal ratchets in 1+1 dimensions, Phys Rev Lett, 77, 12, 2364-2367 (1996)
[42] Constantini, G.; Marchesoni, F., Asymmetric kinks: stabilization by entropic forces, Phys Rev Lett, 87, 114102 (2001)
[43] Denisov, S. I.; . Denisova, E. S.; Hanggi, P., Ratchet transport for a chain of interacting charged particles, Phys Rev E, 71, 016104 (2005)
[44] Cao, J.; . Li, L., Cluster synchronization in an array of hybrid coupled neural networks with delay, Neural Netw., 22, 4, 335-342 (2009) · Zbl 1338.93284
[45] Hasty, J.; Isaacs, F.; Dolnik, M., Designer gene networks: towards fundamental cellular control, Chaos, 11, 207-220 (2001) · Zbl 1029.92011
[46] Chen, C. T., Linear system theory design (1999), Oxford University Press: Oxford University Press USA
[47] Varga, R. S., Ger \(\breve{\operatorname{s}}\) gorin and his circles (2004), Springer-Verlag: Springer-Verlag Berlin
[48] Shapiro, V. E.; Loginov, V. M., ‘Formulae of differentiation’ and their use for solving stochastic equations, Physica A, 91, 563-574 (1978)
[49] Kim, C.; Lee, E. K.; Talkner, P., Numerical method for solving stochastic differential equations with dichotomous noise, Phys Rev E, 73, 026101 (2006)
[50] Nair, M. T.; Singh, A., Linear algebra (2018), Springer: Springer New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.