Dynamic Analysis of a Particle Motion System

This paper formulates a new particle motion system. The dynamic behaviors of the system are studied including the continuous dependence on initial conditions of the system’s solution, the equilibrium stability, Hopf bifurcation at the equilibrium point, etc. This shows the rich dynamic behaviors of the system, including the supercritical Hopf bifurcations, subcritical Hopf bifurcations, and chaotic attractors. Numerical simulations are carried out to verify theoretical analyses and to exhibit the rich dynamic behaviors.

[1]  Ping Zhou,et al.  Hyperchaos, chaos, and horseshoe in a 4D nonlinear system with an infinite number of equilibrium points , 2014 .

[2]  Geoff Boeing,et al.  Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction , 2016, Syst..

[3]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[4]  Zheng-Ming Ge,et al.  Complete identification of chaos of nonlinear nonholonomic systems , 2010 .

[5]  Edson D. Leonel,et al.  Parameter space for a dissipative Fermi–Ulam model , 2011 .

[6]  Anda Xiong,et al.  Classifying and quantifying basins of attraction. , 2015, Chaos.

[7]  Hui-bin Wu,et al.  Dynamic analysis for the hyperchaotic system with nonholonomic constraints , 2017 .

[8]  R. W. Gammon,et al.  Experimental evidence for microscopic chaos , 1998, Nature.

[9]  V. Frolov,et al.  Critical escape velocity for a charged particle moving around a weakly magnetized Schwarzschild black hole , 2013, 1301.4633.

[10]  K. Hashimoto,et al.  Universality in chaos of particle motion near black hole horizon , 2016, 1610.06070.

[11]  Jan Awrejcewicz,et al.  Stick-Slip Dynamics of a Two-Degree-of-Freedom System , 2003, Int. J. Bifurc. Chaos.

[12]  Xinzhi Liu,et al.  Multi-scroll Chaotic and hyperchaotic attractors Generated from Chen System , 2012, Int. J. Bifurc. Chaos.

[13]  Juliano A. de Oliveira,et al.  A family of dissipative two-dimensional mappings: Chaotic, regular and steady state dynamics investigation , 2014 .

[14]  James A. Yorke,et al.  The Many Facets of Chaos , 2015, Int. J. Bifurc. Chaos.

[15]  Davidson,et al.  Chaotic particle dynamics in free-electron lasers. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[16]  Diogo Ricardo da Costa A dissipative Fermi-Ulam model under two different kinds of dissipation , 2015, Commun. Nonlinear Sci. Numer. Simul..

[17]  Petia M. Vlahovska,et al.  Periodic and Chaotic Orbits of Plane-Confined Micro-rotors in Creeping Flows , 2015, J. Nonlinear Sci..

[18]  J. F. Brady,et al.  Chaos and threshold for irreversibility in sheared suspensions , 2005, Nature.

[19]  N. Abbott Colloid Science Collides with Liquid Crystals , 2013, Science.

[20]  Guangyi Wang,et al.  Extreme multistability in a memristor-based multi-scroll hyper-chaotic system. , 2016, Chaos.

[21]  Elizabeth Bradley,et al.  Nonlinear time-series analysis revisited. , 2015, Chaos.