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

Since the famous slow–fast dynamical system referred to as Hodgkin–Huxley model was proposed describe threshold behaviors of neuronal axons, study various and their generation mechanisms has remained a popular topic in modern nonlinear science. The primary purpose this paper is introduce novel transition route induced by comprehensive effect special rest spike bistability timescale difference rather than common bifurcation via modified Chua’s circuit with an external low-frequency excitation. In paper, we attempt explain mechanism behind through quantitative calculations qualitative analyses nonsmooth dynamics on discontinuity boundary. Our work shows that whole responses may tend be complicated when triggered, exhibiting rich even very slight change excitation frequency, which described well using Poincaré maps numerical simulations.