Affiliation:
1. Division of Mathematics, School of Advanced Sciences Vellore Institute of Technology, Chennai Campus Chennai 600 127 Tamil Nadu India
2. School of Mathematical and Statistical Sciences Indian Institute of Technology Mandi Mandi 175 005 Himachal Pradesh India
Abstract
This article is devoted to examine the exponential behavior of stochastic FitzHugh–Nagumo equation in Hilbert space. Initially, the proposed model is reformulated into an abstract space, and the existence of mild solution is constructed by employing Mönch fixed‐point theorem and Hausdorff measure of non‐compactness. Furthermore, suitable conditions are developed to prove the proposed model's exponential behavior which reflects the stable generation and transmission of electric signal in neurons. At last, an example is presented to verify the established theoretical concepts.
Funder
Science and Engineering Research Board
Subject
General Engineering,General Mathematics