期刊
CHAOS SOLITONS & FRACTALS
卷 164, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2022.112669
关键词
FHR model; Slow-fast dynamics; Bifurcation scenarios; Canard phenomenon; MMOs and MMBOs
资金
- National Board for Higher Mathematics (NBHM), India, Department of Atomic Energy, Govt. of India [02011/11/2022NBHM(R.P)/R D-II/10217]
In this study, we explore the complex behavior of neural computation using a biophysically motivated model. We identify the occurrence of mixed mode oscillations (MMOs) and mixed mode bursting oscillations (MMBOs) induced by canard phenomenon, and analyze the bifurcation structure of the system under injected current stimulus. The findings contribute to a better understanding of the rich and complex responses of neurons.
We study the dynamics of a biophysically motivated slow-fast FitzHugh-Rinzel (FHR) model neurons in un-derstanding the complex dynamical behavior of neural computation. We discuss the mathematical frameworks of diverse excitabilities and repetitive firing responses due to the applied stimulus using the slow-fast system. The results focus on the multiple time scale dynamics that include canard phenomenon induced mixed mode oscillations (MMOs) and mixed mode bursting oscillations (MMBOs). The bifurcation structure of the system is examined with injected current stimulus as the relevant parameter. We use the folded node theory to study the canards near the fold points. Further, we demonstrate the homoclinic bifurcation and the transition route to chaos through MMOs. It helps us in understanding the fundamentals of such complex rich neuronal responses. To show the chaotic nature in certain parameter regime, we compute the Lyapunov spectrum as a function of time and predominant parameter, I, that establishes our findings. Finally, we conclude that our observed results may have major significance and discuss the potential applications of MMOs in neural dynamics.
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