1:2 and 1:4 resonances in a two-dimensional discrete Hindmarsh–Rose model
1:2 and 1:4 resonances in a two-dimensional discrete Hindmarsh–Rose model
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DOI：
10.1007/s11071-014-1696-3
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发表时间：
2015
影响因子：
5.6
通讯作者：
Bo Li;Zhimin He
中科院分区：
文献类型：
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作者：
Bo Li;Zhimin He
本文讨论了二维离散 Hindmarsh-Rose 模型的二参数分岔。利用一系列仿射变换和分岔理论表明系统会发生 1:2 和 1:4 共振。三维空间中两个不同变化参数的数值模拟包括相图、二参数分岔图和最大李雅普诺夫指数图，不仅说明了理论分析，而且展示了有趣且复杂的动力学行为。
In this paper, the two-parameter bifurcations of a two-dimensional discrete Hindmarsh–Rose model is discussed. It is shown that the system undergoes 1:2 and 1:4 resonances by using a series of affine transformations and bifurcation theory. The numerical simulations including phase portraits, two-parameter bifurcation diagrams, and maximum Lyapunov exponents diagrams for two different varying parameters in a three-dimensional space, not only illustrate the theoretical analysis, but also display the interesting and complex dynamical behaviors.