A note on explicit solutions of FitzHugh-Rinzel system
Monica De Angelis
TL;DR
This paper derives explicit traveling wave solutions for the FitzHugh-Rinzel system, enhancing understanding of its complex biological dynamics by explicitly incorporating the effects of diffusion.
Contribution
It introduces a class of explicit traveling wave solutions for the FitzHugh-Rinzel system, highlighting the impact of diffusion on its behavior.
Findings
Explicit traveling wave solutions derived
Diffusion term's contribution demonstrated
Enhanced understanding of biological system dynamics
Abstract
The numerous scientific feedbacks that the FitzHugh-Rinzel system (FHR) is having in various scientific fields, lead to further studies on the determination of its explicit solutions. Indeed, such a study can help to get a better understanding of several behaviors in the complex dynamics of biological systems. In this note, a class of traveling wave solutions is determined and specific solutions are achieved to explicitly show the contribution due to a diffusion term considered in the FHR model.
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Nonlinear Dynamics and Pattern Formation · Mathematical Biology Tumor Growth