Boundary-Crisis-Induced Complex Bursting Patterns in a Forced Cubic Map
Boundary-Crisis-Induced Complex Bursting Patterns in a Forced Cubic Map
复制标题
强制三次映射中边界危机引发的复杂爆发模式
DOI：
10.1142/s0218127417500511
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发表时间：
2017
影响因子：
2.2
通讯作者：
Bi Qinsheng
中科院分区：
文献类型：
--
作者：
Han Xiujing;Zhang Chun;Yu Yue;Bi Qinsheng
本文报告了基于强制立方图的复杂爆发模式的新途径，其中研究了边界危机引发的新爆发模式。通常，三次映射表现出固定点的稳定上分支和下分支，这些分支可能会通过一系列倍周期分岔而演变成相反参数方向的混沌。我们表明，稳定分支上的混沌吸引子可能会因边界危机而突然消失，从而导致从混沌到其他吸引子的快速过渡，并引起三次映射解的稳定分支之间的切换。特别是，边界危机引起的轨迹切换的吸引子可以是不动点、周期轨道和混沌，这取决于立方映射的参数值，这有助于我们揭示边界危机引发的爆发的三种一般类型，即混沌点型爆发、混沌循环型爆发和混沌-混沌型爆发。此外，每种突发类型可能包含不同的b...
This paper reports novel routes to complex bursting patterns based on a forced cubic map, in which boundary-crisis-induced novel bursting patterns are investigated. Typically, the cubic map exhibits stable upper and lower branches of fixed points, which may evolve into chaos in opposite parameter directions by a cascade of period-doubling bifurcations. We show that the chaotic attractors on the stable branches may suddenly disappear by boundary crisis, thus leading to fast transitions from chaos to other attractors and giving rise to switchings between the stable branches of solutions of the cubic map. In particular, the attractors that the trajectory switches to by boundary crisis can be fixed points, periodic orbits and chaos, dependent on parameter values of the cubic map, and this helps us to reveal three general types of boundary-crisis-induced bursting, i.e. bursting of chaos-point type, bursting of chaos-cycle type and bursting of chaos-chaos type. Moreover, each bursting type may contain various b...