Slow–Fast Dynamics Behaviors under the Comprehensive Effect of Rest Spike Bistability and Timescale Difference in a Filippov Slow–Fast Modified Chua’s Circuit Model
Slow–Fast Dynamics Behaviors under the Comprehensive Effect of Rest Spike Bistability and Timescale Difference in a Filippov Slow–Fast Modified Chua’s Circuit Model
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DOI：
10.3390/math10234606
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发表时间：
2022-12
期刊：
影响因子：
2.4
通讯作者：
Shaolong Li;Weipeng Lv;Zhenyang Chen;Miao Xue;Qinsheng Bi
中科院分区：
文献类型：
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作者：
Shaolong Li;Weipeng Lv;Zhenyang Chen;Miao Xue;Qinsheng Bi
自从著名的慢-快动力学系统霍奇金-赫胥黎模型被提出来描述神经元轴突的阈值行为以来，各种慢-快动力学行为及其生成机制的研究一直是现代非线性科学的热门话题。本文的主要目的是通过带有外部低频激励的修改蔡氏电路模型引入一种由特殊静息尖峰双稳态和时标差异的综合效应引起的新颖的过渡路线，而不是常见的分岔。在本文中，我们试图通过不连续边界上的非光滑动力学的定量计算和定性分析来解释这种新颖的过渡路线背后的动力学机制。我们的工作表明，当该过渡路线被触发时，整个系统的响应可能趋于多样化和复杂，即使激励频率发生非常微小的变化，也表现出丰富的慢-快动力学行为，这在数值模拟中使用庞加莱图可以很好地描述。
Since the famous slow–fast dynamical system referred to as the Hodgkin–Huxley model was proposed to describe the threshold behaviors of neuronal axons, the study of various slow–fast dynamical behaviors and their generation mechanisms has remained a popular topic in modern nonlinear science. The primary purpose of this paper is to introduce a novel transition route induced by the comprehensive effect of special rest spike bistability and timescale difference rather than a common bifurcation via a modified Chua’s circuit model with an external low-frequency excitation. In this paper, we attempt to explain the dynamical mechanism behind this novel transition route through quantitative calculations and qualitative analyses of the nonsmooth dynamics on the discontinuity boundary. Our work shows that the whole system responses may tend to be various and complicated when this transition route is triggered, exhibiting rich slow–fast dynamics behaviors even with a very slight change in excitation frequency, which is described well by using Poincaré maps in numerical simulations.