[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.

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.

BisPhysicochemical, Bacteriological, Well-Water, Plasmid, Resistance, Bacteria, Gene, Antibioticstable Dynamic System, Bifurcation Parameter, Periodic Attractor, Chaos

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