Severino H. da Silva . Hugo Saraiva Tavares

Unidade Acadˆemica de Matem´atica, Universidade Federal de Campina Grande, 58051-900 Campina Grande PB, Brazil, E-mails: horacio@mat.ufcg.edu.br;horaciusp@gmail.com Instituto de F´ısica-IF/UFRJ, Avenida Athos da Silveira Ramos, 149 - Centro de Tecnologia - Bloco A, Rio de Janeiro - RJ, Brazil, E-mail: hugoczpb@gmail.com

Received in final form on March 18, 2023

Abstract
In this paper, we explore a non-local evolution equation commonly used in models of neuronal activity, represented by ∂η(x, t) /∂t = −η(x, t) + J ∗ (f ◦ η)(x, t) + h(x), where h(x) > 0. We demonstrate the existence of nontrivial periodic equilibrium solutions under reasonable assumptions about the functions f, J, and h. For this purpose, we utilize an energy functional and the LaSalle's Invariance Principle.

Keywords
Periodic Equilibrium Solution, Global Attractor, Lyapunov Functional, Neural Field, Nonlocal Evolution Equation, LaSalle’s Invariance Principle.

Cite This Article
Severino H. da Silva . Hugo Saraiva Tavares,Existence of Nontrivial Periodic Equilibrium Solutions for Neural Field Equations, J. Innovation Sciences and Sustainable Technologies, 3(2)(2023), 99 - 107. https://doie.org/10.0725/JISST.2023342568

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