Bifurcation and chaos in discrete FitzHugh–Nagumo system ☆
Bifurcation and chaos in discrete FitzHugh–Nagumo system ☆
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DOI：
10.1016/j.chaos.2003.12.043
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发表时间：
2004-07
影响因子：
7.8
通讯作者：
Zhujun Jing;Yu Chang;B. Guo
中科院分区：
文献类型：
--
作者：
Zhujun Jing;Yu Chang;B. Guo
研究了用欧拉方法得到的离散FitzHugh-Nagumo方程组。利用中心流形定理和分支理论，导出了系统的折叠分支、翻转分支和Hopf分支存在的条件，证明了系统在Marotto混沌定义意义下的混沌行为。数值模拟结果不仅与理论分析一致，而且显示了新的有趣的动力学行为，包括吸引不变圆、周期3、周期6、周期7、周期9、周期15、周期20、周期21和周期n轨道，周期3的倍周期分岔逆级联，周期9的倍周期分岔级联，15、20和21，内部和外部危机现象，不稳定性机制，周期窗口中的瞬态混沌，吸引和非吸引混沌吸引子。李雅普诺夫指数的计算证实了混沌行为。
The discrete FitzHugh–Nagumo system obtained by Euler method is investigated. The conditions of existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, chaotic behavior in the sense of Marotto’s definition of chaos is proved. And numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamical behaviors, including attracting invariant circle, period-3, period-6, period-7, period-9, period-15, period-20, period-21, and period-n orbits, an inverse cascade of period-doubling bifurcation in period-3, cascade of period-doubling bifurcation in periods-9, 15, 20 and 21, interior and exterior crisis phenomena, intermittency mechanic, transient chaos in period-window, attracting and non-attracting chaotic attractors. The computations of Lyapunov exponents confirm the chaotic behaviors.