Existence of nonstationary periodic solutions for $\Gamma$-symmetric Lotka-Volterra type systems

Abstract

In this paper we present a general framework for applications of the twisted equivariant degree (with one free parameter) to an autonomous $\Gamma$-symmetric system of functional differential equations in order to detect and classify (according to their symmetric properties) its periodic solutions. As an example we establish the existence of multiple non-constant periodic solutions of delay Lotka-Volterra equations with $\Gamma$-symmetries. We also include some computational examples for several finite groups $\Gamma$.