International Journal of Modern Physics and Applications
Articles Information
International Journal of Modern Physics and Applications, Vol.5, No.2, Jun. 2019, Pub. Date: May 31, 2019
Multistable Dynamic Response Behavior of Two-dimensional Discrete Duffing System
Pages: 11-16 Views: 1356 Downloads: 355
Authors
[01] Luman Wang, College of Mathematics and Computer Science, Zhejiang Normal University, P. R. China.
[02] Haixia Fu, College of Mathematics and Computer Science, Zhejiang Normal University, P. R. China.
[03] Dongmei Yan, College of Mathematics and Computer Science, Zhejiang Normal University, P. R. China.
[04] Youhua Qian, College of Mathematics and Computer Science, Zhejiang Normal University, P. R. China.
Abstract
Multi-time scale problems are ubiquitous in natural science. While slow-varying parameter is one of the typical symbols of multiple-time scale. However, there is few research on the phenomenon of periodic catastrophe. In this paper, we study the multistable dynamic response behavior of the discrete fast-slow coupled Duffing system. In addition, we observe a pair of critical parameter values, which result in the disappearance of period-1 attractor under some certain parameters and the bistable dynamic behavior appears in which the periodic attractor and the chaotic attractor coexisted near the critical value. When the bifurcation parameter passes through critical points, the system will jump, which may lead to the transition from period-1 attractor to previous coexisting attractor, thus bistability is destroyed and system gets into mono-stasis. We obtain the bifurcation charts and time history curve of the bistable dynamic system for the coexistence of period-1 attractor and periods-1, 2, 4 attractors and chaos in the critical range. When the critical value range is exceeded, the period-1 attractor disappears, which leads to the bistable imbalance. Our results enrich the bistable dynamical mechanisms in discrete systems.
Keywords
BisPhysicochemical, Bacteriological, Well-Water, Plasmid, Resistance, Bacteria, Gene, Antibioticstable Dynamic System, Bifurcation Parameter, Periodic Attractor, Chaos
References
[01] Arecchi F T, Badii R, Politi A. Generalized multistability and noise-induced jumps in a nonlinear dynamical system. Physical Review A, 1985, 32 (1): 402-408.
[02] Arecchi F T, Badii R, Politi A. Low-frequency phenomena in dynamical systems with many attractors. Physical Review A, 1984, 29 (2): 1006-1009.
[03] Mason J P. Noninvasive control of stochastic resonance and an analysis of multistable oscillators. Histopathology, 2001, 22 (4): 343-347.
[04] Liu Y, ChSvez J P. Controlling multistability in a vibro-impact capsule system. Nonlinear Dynamics, 2016, 88 (2): 1289-1304.
[05] Kengne J, Chedjou J C, Kom M, et al. Regular oscillations, chaos, and multistability in a system of two coupled van der Pol oscillators: numerical and experimental studies. Nonlinear Dynamics, 2014, 76 (2): 1119-1132.
[06] Arecchi F T, Meucci R, Puccioni G, et al. Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser. Physical Review Letters, 1982, 49 (17): 1217.
[07] Luo X S, Chen G, Wang B H, et al. Hybrid control of period-doubling bifurcation and chaos in discrete nonlinear dynamical systems. Chaos Solitons and Fractals, 2003, 18 (4): 775-783.
[08] Jing Z J, Wang R Q. Complex dynamics in Duffing system with two external forcings. Chaos Solitons and Fractals, 2005, 23 (2): 399-411.
[09] Yang X D, Chen L Q. Bifurcation and chaos of an axially accelerating viscoelastic beam. Chaos Solitons and Fractals, 2005, 23 (1): 249-258.
[10] Jing Z J, Yang J P. Bifurcation and chaos in discrete-time predatorıprey system. Chaos Solitons and Fractals, 2006, 27 (1): 259-277.
[11] Shrimali Manish Dev, Prasad Awadhesh, Ramaswamy Ram, Feudel Ulrike. The Nature of Attractor Basins in Multistable Systems. International Journal of Bifurcation and Chaos, 2008, 18 (06): 1675-1688.
[12] Cang S J, Qi G Y, Chen Z Q. A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system. Nonlinear Dynamics, 2010, 59 (3): 515-527.
[13] Hens C R, Banerjee R, Feudel U, et al. How to obtain extreme multistability in coupled dynamical systems. Physical Review E, 2012, 85 (2): 035202.
[14] Pal S, Sahoo B, Poria S. A generalized scheme for designing multistable continuous dynamical systems. Pramana, 2016, 86 (6): 1183-1193.
[15] Chen Z Q, Wang J L, Li Y. Research on the bifurcation and chaos of a two-degree-of-freedom discrete Duffing-Holmes system. Journal of Dynamics and Control, 2017, 15 (4): 324-329. (Chinese edition).
[16] Han X, Yu Y, Zhang C, et al. Turnover of hysteresis determines novel bursting in Duffing system with multiple-frequency external forcings. International Journal of Non-Linear Mechanics, 2017, 89: 69-74.
[17] Han X J, Zhang C, Yu Y, et al. Boundary-Crisis-Induced Complex Bursting Patterns in a Forced Cubic Map. International Journal of Bifurcation and Chaos, 2017, 27 (4): 1750051.
[18] Chakraborty P. A scheme for designing extreme multistable discrete dynamical systems. Pramana, 2017, 89 (3), DOI: 10.1007/s12043-017-1431-y.
[19] Zhang X F, Wu L, Bi Q S. Structural characteristics analysis of compound mode oscillations under different excitation frequency ratios. Science in China: Technical Science, 2017 (6): 666-674. (Chinese edition).
[20] Wiggers V, Rech P C. Multistability and organization of periodicity in a van der Pol Duffing oscillator. Chaos Solitons and Fractals, 2017, 103: 632-637.
[21] Chen Z Y, Han X J, Bi Q S. Complex relaxation oscillations in discrete Duffing mapping induced by a boundary shock. Journal of Mechanics, 2017, 49 (6): 1380-1389. (Chinese edition).
[22] Han X J, Wei M K, Bi Q S, et al. Obtaining amplitude-modulated bursting by multiple-frequency slow parametric modulation. Physical Review E, 2018, 97 (1), DOI: 10.1103/PhysRevE.97.012202.
600 ATLANTIC AVE, BOSTON,
MA 02210, USA
+001-6179630233
AIS is an academia-oriented and non-commercial institute aiming at providing users with a way to quickly and easily get the academic and scientific information.
Copyright © 2014 - American Institute of Science except certain content provided by third parties.