Emergence of Canard induced mixed mode oscillations in a slow–fast dynamics of a biophysical excitable model

Sanjeev Kumar Sharma, Arnab Mondal, Argha Mondal, M.A. Aziz-Alaoui, Ranjit Kumar Upadhyay and Jun Ma

Chaos, Solitons & Fractals, 2022, vol. 164, issue C

Abstract: We study the dynamics of a biophysically motivated slow–fast FitzHugh–Rinzel (FHR) model neurons in understanding 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.

Keywords: FHR model; Slow–fast dynamics; Bifurcation scenarios; Canard phenomenon; MMOs and MMBOs (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008487

DOI: 10.1016/j.chaos.2022.112669

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