Dynamic behavior for a three-coupled FitzHugh–Rinzel model with delays

Document Type : Research Paper

Author

Department of Mathematics and Computer Science, Alabama State University, Montgomery, USA

Abstract

This paper investigates the dynamic behavior of a three-coupled FitzHugh Rinzel (FHR) model with time delays. We extend the result in the literature from a two-coupled FHR model to a three-coupled FHR model. Using the method of mathematical analysis, the original system has been linearized. The unique equilibrium point of the original system has been changed to a trivial equilibrium point of the linearized system. The instability of the trivial equilibrium point of the linearized system implies the instability of the original equilibrium point. The instability of the unique equilibrium point and the boundedness of the solutions will force this system to generate a periodic solution. The periodic oscillation of the three-coupled FHR model with time delays has been discussed. Some sufficient conditions to guarantee the oscillation of the solutions are provided, and computer simulations are given to support the present criteria.

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References

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Journal of Mahani Mathematical Research
Volume 15, Issue 1 - Serial Number 33
January 2026
Pages 447-460

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History

  • Receive Date: 23 March 2025
  • Revise Date: 05 August 2025
  • Accept Date: 02 October 2025

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