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Chaotic study on a multibody interacting particle system with trajectory of variable curvature radius. (English) Zbl 07261589
Summary: Multibody interacting particle system is one of the most important driven-diffusive systems, which can well describe stochastic dynamics of self-driven particles unidirectionally updating along one-dimensional discrete lattices controlled by hard-core exclusions. Such determined nonlinear dynamic system shows the chaos, a complicated motion that is similar to random and can’t determine future states according to given initial conditions. Derived from the study of randomness in the framework of determinism, chaos effectively unifies determinacy and randomness of nonlinear physics, which also embodies the randomness and uncertainty of multi-body particle motions. Besides, chaos often presents complex ordered phenomena like aperiodic ordered motion state etc., which indicates it’s a stable coordination of local random and global mode. Different with previous work, a mesoscopic multibody interacting particle system considering the trajectory of variable curvature radius is proposed, which is more reliable to depict true driven-diffusive systems. Nonlinear dynamical master equations are established. Linear and nonlinear stability analyses are performed to test system robustness, which lead to linear stable region, metastable region, unstable region, triangular wave, solitary wave and kink-antikink wave. Complete numerical simulations under quantitatively changing characteristic order parameters are performed to reveal intrinsic chaotic dynamics mechanisms. By comparing fruitful chaotic patterns, double periodic convergence in stable limit cycles is observed due to attractors folding. System states tend to be limit cycles with the passage of time. The longer time is, the higher density is near attractors. The number of main components of attractors and the shape of them are found to drastically change with these parameters. Hereafter, the chaotic formation mechanism is explained by performing Fourier spectrums analyses. High and low frequency elements are obtained, whose module lengths are found to change periodically with time and nonperiodically with space. Our results show the sensitivity of the chaotic system to initial conditions, which mean slight changes of initial states in one part of system can lead to disproportionate consequences in other parts. The sensitivity is directly related to uncertainty and unpredictability. Moreover, calculations also show that three kinds of attractors (namely, point attractor, limit-cycle attractor and strange attractor) exist in the proposed chaotic system, which control particle motions. The first two attractors are convergence attractors playing a limiting role, which lead to static and balanced features of system. Oppositely, strange attractor makes the system deviate from regions of convergent attractors and creates unpredictability by inducing the vitality of the system and turning it into a non-preset mode. Furthermore, interactions between convergence attractors and strange attractors trigger such locally fruitful modes. This work will be helpful to understand mesoscopic dynamics, stochastic dynamics and non-equilibrium dynamical behaviors of multibody interacting particle systems.
MSC:
70 Mechanics of particles and systems
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[1] Scholz, C.; Jahanshahi, S.; Ldov, A., Inertial delay of self-propelled particles, Nat Commun, 9, 1, 5156 (2018)
[2] Yan, J.; Han, M.; Zhang, J., Reconfiguring active particles by electrostatic imbalance, Nat Mater, 15, 10, 1095 (2016)
[3] Suzuki, R.; Weber, C. A.; Frey, E., Polar pattern formation in driven filament systems requires non-binary particle collisions, Nat Phys, 11, 10, 839 (2015)
[4] Helbing, D., Traffic and related self-driven many-particle systems, Rev Mod Phys, 73, 4, 1067 (2001)
[5] Chou, T.; Mallick, K.; RKP, Z., Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport, Rep Prog Phys, 74, 11, 116601 (2011)
[6] Lü, X.; Ma, W. X.; Yu, J.; Khalique, C. M., Solitary waves with the Madelung fluid description: a generalized derivative nonlinear Schrödinger equation, Commun Nonlinear Sci, 31, 1-3, 40-46 (2016)
[7] Chai, J.; Tian, B.; Zhen, H. L.; Sun, W. R.; Liu, D. Y., Dynamic behaviors for a perturbed nonlinear Schrödinger equation with the power-law nonlinearity in a non-kerr medium, Commun Nonlinear Sci, 45, 93-103 (2017)
[8] Huepe, C.; Aldana, M., Intermittency and clustering in a system of self-driven particles, Phys Rev Lett, 92, 16, 168701 (2004)
[9] Lü, X.; Lin, F., Soliton excitations and shape-changing collisions in alpha helical proteins with interspine coupling at higher order, Commun Nonlinear Sci, 32, 241-261 (2016)
[10] Du, Z.; Tian, B.; Chai, H. P.; Yuan, Y. Q., Vector multi-rogue waves for the three-coupled fourth-order nonlinear Schrödinger equations in an alpha helical protein, Commun Nonlinear Sci, 67, 49-59 (2019)
[11] Oorni, K.; Pentikainen, M. O.; Ala-Korpela, M.; Kovanen, P. T., Aggregation, fusion, and vesicle formation of modified low density lipoprotein particles: molecular mechanisms and effects on matrix interactions, J Lip Res, 41, 11, 1703-1714 (2000)
[12] Marchetti, M. C.; Joanny, J. F.; Ramaswamy, S.; Liverpool, T. B.; Prost, J.; Rao, M.; Simha, R. A., Hydrodynamics of soft active matter, Rev Mod Phys, 85, 3, 1143 (2013)
[13] Tome, T.; Oliveira, M. J., Nonequilibrium model for the contact process in an ensemble of constant particle number, Phys Rev lett, 86, 25, 5643 (2001)
[14] Wang, Y. Q.; Wang, J. W.; Zhu, Z. A.; Wang, B. H., Stochastic dynamics in nonequilibrium phase transitions of multiple totally asymmetric simple exclusion processes coupled with strong and weak interacting effects, Int J Mod Phys B, 33, 20, 1950229 (2019)
[15] Jiang, R.; Wang, Y. Q.; Kolomeisky, A. B.; Huang, W.; Hu, M. B.; Wu, Q. S., Phase diagram structures in a periodic one-dimensional exclusion process, Phys Rev E, 87, 1, 012107 (2013)
[16] Wang, Y. Q.; Wang, J. W.; Wang, B. H., Physical mechanisms in impacts of interaction factors on totally asymmetric simple exclusion processes, Int J Mod Phys B, 33, 20, 1950217 (2019) · Zbl 1428.82042
[17] Gao, X. Y., Mathematical view with observational/experimental consideration on certain (2+1)-dimensional waves in the cosmic/laboratory dusty plasmas, Appl Math Lett, 91, 165-172 (2019) · Zbl 1445.76101
[18] Wang, M.; Tian, B.; Sun, Y.; Yin, H. M.; Zhang, Z., Mixed lump-stripe, bright rogue wave-stripe, dark rogue wave-stripe and dark rogue wave solutions of a generalized Kadomtsev-Petviashvili equation in fluid mechanics, Chinese J Phys, 60, 440-449 (2019)
[19] Zhao, X. H.; Tian, B.; Xie, X. Y.; Wu, X. Y.; Sun, Y.; Guo, Y. J., Solitons, bäcklund transformation and lax pair for a (2+1)-dimensional davey-stewartson system on surface waves of finite depth, Wave Random Complex, 28, 2, 356-366 (2018)
[20] Yuan, Y. Q.; Tian, B.; Liu, L.; Wu, X. Y.; Sun, Y., Solitons for the (2+1)-dimensional Konopelchenko-Dubrovsky equations, J Math Anal Appl, 460, 1, 476-486 (2018) · Zbl 1384.35110
[21] Wang, Y. Q.; Zhang, Z. H., Cluster mean-field dynamics in one-dimensional TASEP with inner interactions and Langmuir dynamics, Mod Phys Lett B, 33, 2, 1950012 (2019)
[22] Du, Z.; Tian, B.; Chai, H. P.; Sun, Y.; Zhao, X. H., Rogue waves for the coupled variable-coefficient fourth-order nonlinear Schrödinger equations in an inhomogeneous optical fiber, Chaos Soliton Fract, 109, 90-98 (2018) · Zbl 1390.35323
[23] Zhang, C. R.; Tian, B.; Wu, X. Y.; Yuan, Y. Q.; Du, X. X., Rogue waves and solitons of the coherently-coupled nonlinear Schrödinger equations with the positive coherent coupling, Phys Scripta, 93, 9, 95202 (2018)
[24] Wang, Y. Q.; Zhou, C. F.; Wang, J. W.; Ni, X. P., Evolvement laws and stability analyses of traffic network constituted by changing ramps and main road, Int J Mod Phys B, 33, 20, 1950228 (2019) · Zbl 1428.90039
[25] Du, X. X.; Tian, B.; Wu, X. Y.; Yin, H. M.; Zhang, C. R., Lie group analysis, analytic solutions and conservation laws of the (3+1)-dimensional Zakharov-Kuznetsov-burgers equation in a collisionless magnetized electron-positron-ion plasma, Eur Phys J Plus, 133, 9, 378 (2018)
[26] Hu, C. C.; Tian, B.; Wu, X. Y.; Yuan, Y. Q.; Du, Z., Mixed lump-kink and rogue wave-kink solutions for a (3+1)-dimensional b-type kadomtsev-petviashvili equation in fluid mechanics, Eur Phys J Plus, 133, 2, 40 (2018)
[27] Wang, Y. Q.; Chu, X. J.; Zhou, C. F.; Yan, B. W.; Jia, B.; Fang, C. H., Wave dynamics in an extended macroscopic traffic flow model with periodic boundaries, Mod Phys Lett B, 32, 16, 1850168 (2018)
[28] Chen, S. S.; Tian, B.; Liu, L.; Yuan, Y. Q.; Zhang, C. R., Conservation laws, binary darboux transformations and solitons for a higher-order nonlinear schrödinger system, Chaos Soliton Fract, 118, 337-346 (2019)
[29] Chai, J.; Tian, B.; Xie, X. Y.; Sun, Y., Conservation laws, bilinear bäcklund transformations and solitons for a nonautonomous nonlinear Schrödinger equation with external potentials, Commun Nonlinear Sci, 39, 472-480 (2016)
[30] Gao, L. N.; Zi, Y. Y.; Yin, Y. H.; Ma, W. X.; Lü, X., Bäcklund transformation, multiple wave solutions and lump solutions to a (3+1)-dimensional nonlinear evolution equation, Nonlinear Dyn, 89, 2233-2240 (2017)
[31] Wang, Y. Q.; Yan, B. W.; Zhou, C. F.; Li, W. K.; Jia, B., Bifurcation analysis of a heterogeneous traffic flow model, Mod Phys Lett B, 32, 9, 1850118 (2018)
[32] Gao, X. Y.; Guo, Y. J.; Shan, W. R., Water-wave symbolic computation for the earth, enceladus and titan: higher-order boussinesq-burgers system, auto-and non-auto-bäcklund transformations, App Math Lett, 106170 (2019)
[33] Lü, X., Bright-soliton collisions with shape change by intensity redistribution for the coupled sasa-satsuma system in the optical fiber communications, Commun Nonlinear Sci, 19, 11, 3969-3987 (2014) · Zbl 07175188
[34] Wu, X. Y.; Tian, B.; Liu, L.; Sun, Y., Bright and dark solitons for a discrete (2+1)-dimensional Ablowitz-ladik equation for the nonlinear optics and bose-einstein condensation, Commun Nonlinear Sci, 50, 201-210 (2017)
[35] Chai, H. P.; Tian, B.; Du, Z., Localized waves for the mixed coupled Hirota equations in an optical fiber, Commun Nonlinear Sci, 70, 181-192 (2019)
[36] Xie, X. Y.; Tian, B.; Liu, L.; Guan, Y. Y.; Jiang, Y., Bright solitons for a generalized nonautonomous nonlinear equation in a nonlinear inhomogeneous fiber, Commun Nonlinear Sci, 47, 16-22 (2017)
[37] Wang, Y. Q.; Zhou, C. F.; Jia, B.; Zhu, H. B., Reliability analysis of degradable networks with modified BPR, Mod Phys Lett B, 31, 36, 1750353 (2017)
[38] Vicsek, T.; Czirok, A.; Ben-Jacob, E., Novel type of phase transition in a system of self-driven particles, Phys Rev Lett, 75, 6, 1226 (1995)
[39] Wang, Y. Q.; Jiang, R.; Wu, Q. S., Dynamics in phase transitions of TASEP coupled with multi-lane SEPs, Nonlinear Dyn, 88, 3, 1631-1641 (2017)
[40] Wang, Y. Q.; Wang, J. X.; Li, W. H., Analytical and simulation studies of driven diffusive system with asymmetric heterogeneous interactions, Sci Rep-UK, 8, 1, 16287 (2018)
[41] Wang, Y. Q.; Jiang, R.; Kolomeisky, A. B.; Hu, M. B., Bulk induced phase transition in driven diffusive systems, Sci Rep-UK, 4, 5459 (2014)
[42] Derrida, B.; Evans, M. R.; Hakim, V., Exact solution of a 1d asymmetric exclusion model using a matrix formulation, J Phys A, 26, 7, 1493 (1993) · Zbl 0772.60096
[43] RKP, Z., Twenty five years after KLS: a celebration of non-equilibrium statistical mechanics, J Stat Phys, 138, 1-3, 20-28 (2010) · Zbl 1186.82053
[44] Czirok, A.; Stanley, H. E.; Vicsek, T., Spontaneously ordered motion of self-propelled particles, J Phys A, 30, 5, 1375 (1997)
[45] Czirok, A.; Vicsek, T., Collective behavior of interacting self-propelled particles, Physica A, 281, 1-4, 17-29 (2000)
[46] Degond, P.; Motsch, S., Macroscopic limit of self-driven particles with orientation interaction, Comp Ren Math, 345, 10, 555-560 (2007) · Zbl 1206.82068
[47] Degond, P.; Motsch, S., Continuum limit of self-driven particles with orientation interaction, Math Mod Meth Appl S, 18, 1193-1215 (2008) · Zbl 1157.35492
[48] Wan, M. B.; CJO, R.; Nussinov, Z., Rectification of swimming bacteria and self-driven particle systems by arrays of asymmetric barriers, Phys Rev Lett, 101, 1, 018102 (2008)
[49] Wang, Y. Q.; Jia, B.; Jiang, R., Dynamics in multi-lane TASEPs coupled with asymmetric lane-changing rates, Nonlinear Dyn, 88, 3, 2051-2061 (2017) · Zbl 1380.90086
[50] Lü, X.; Peng, M., Systematic construction of infinitely many conservation laws for certain nonlinear evolution equations in mathematical physics, Commun Nonlinear Sci, 18, 9, 2304-2312 (2013) · Zbl 1304.35030
[51] Sun, W. R.; Tian, B.; Xie, X. Y.; Chai, J.; Jiang, Y., High-order rogue waves of the coupled nonlinear Schrödinger equations with negative coherent coupling in an isotropic medium, Commun Nonlinear Sci, 39, 538-544 (2016)
[52] Shan, W. R.; Yan, T. Z.; Lü, X., Analytic study on the sawadaCKotera equation with a nonvanishing boundary condition in fluids, Commun Nonlinear Sci, 18, 7, 1568-1575 (2013) · Zbl 1311.35264
[53] Xu, H. N.; Ruan, W. Y.; Lü, X., Multi-exponential wave solutions to two extended Jimbo-Miwa equations and the resonance behavior, Appl Math Lett, 99, 105976 (2020) · Zbl 1448.35459
[54] Hua, Y. F.; Guo, B. L.; Ma, W. X.; Lü, X., Interaction behavior associated with a generalized (2+1)-dimensional hirota bilinear equation for nonlinear waves, Appl Math Model, 74, 184-198 (2019)
[55] Gai, X. L.; Gao, Y. T.; Wang, L.; Meng, D. X.; Lü, X.; Sun, Z. Y.; Yu, X., Painlevé property, lax pair and darboux transformation of the variable-coefficient modified kortweg-de vries model in fluid-filled elastic tubes, Commun Nonlinear Sci, 16, 4, 1776-1782 (2011) · Zbl 1221.35334
[56] Yin, Y. H.; Ma, W. X.; Liu, J. G.; Lü, X., Diversity of exact solutions to a (3+1)-dimensional nonlinear evolution equation and its reduction, Comput Math Appl, 76, 6, 1275-1283 (2018) · Zbl 1434.35172
[57] Chen, S. J.; Yin, Y. H.; Ma, W. X.; Lü, X., Abundant exact solutions and interaction phenomena of the (2+1)-dimensional YTSF equation, Anal Math Phys, 9, 4, 2329-2344 (2019) · Zbl 1448.35441
[58] Lauga, E.; DiLuzio, W. R.; Whitesides, G. M.; Stone, H. A., Swimming in circles: motion of bacteria near solid boundaries, Biophys J, 90, 2, 400-412 (2006)
[59] McCloskey, M.; Caramazza, A.; Green, B., Curvilinear motion in the absence of external forces: naive beliefs about the motion of objects, Science, 210, 4474, 1139-1141 (1980)
[60] Wang, Y. Q.; Zhou, C. F.; Li, W. K., Stability analysis and wave dynamics of an extended hybrid traffic flow model, Mod Phys Lett B, 32, 05, 1850055 (2018)
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