Chaotic study on a multibody interacting particle system with trajectory of variable curvature radius

Abstract

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.