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

Shaolong Li, Weipeng Lv, Zhenyang Chen, Miao Xue and Qinsheng Bi ()
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Shaolong Li: Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
Weipeng Lv: Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
Zhenyang Chen: Faculty of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China
Miao Xue: School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China
Qinsheng Bi: Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China

Mathematics, 2022, vol. 10, issue 23, 1-21

Abstract: 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.

Keywords: rest spike bistability; slow–fast decomposition analysis; multi-period mixed bursting phenomena; coexisting whole system responses (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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