A priori estimates for solutions of FitzHugh-Rinzel system
Monica De Angelis
TL;DR
This paper derives a priori estimates for solutions of the FitzHugh-Rinzel system, a model describing biological phenomena like bursting oscillations, by expressing solutions through integral equations and analyzing the fundamental solution.
Contribution
It introduces a method to obtain a priori estimates for solutions of the FitzHugh-Rinzel system using integral equations and properties of the fundamental solution.
Findings
Established a priori bounds for solutions in the whole space.
Demonstrated the influence of initial data and source terms on solutions.
Provided a framework for analyzing complex biological dynamics.
Abstract
The FitzHugh-Rinzel system is able to describe some biophysical phenomena, such as bursting oscillations, and the study of its solutions can help to better understand several behaviours of the complex dynamics of biological systems. We express the solutions by means of an integral equation involving the fundamental solution related to a non linear integro-differential equation. Properties of allow us to obtain a priori estimates for solutions determined in the whole space, showing both the influence of the initial data and the source term.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.