Heteroclinic networks in an ensemble of generalized Lotka-Volterra elements

TL;DR

This paper investigates heteroclinic networks within a generalized Lotka-Volterra model of four coupled elements, revealing the existence and parameter conditions for various heteroclinic structures in the system.

Contribution

It identifies and characterizes heteroclinic networks in a four-element generalized Lotka-Volterra system, providing a parameter space partition for their existence.

Findings

Existence of heteroclinic networks in the model.

Partition of coupling parameter space for different heteroclinic structures.

Conditions for the formation of heteroclinic cycles.

Abstract

In this article the generalized Lotka-Volterra model of ensemble of four excitory or inhibitory coupled elements are studied. It is shown that in the phase space of the model there exist heteroclinic network: a connected union of two or more heteroclinic cycles. A partition of the plane of coupling parameters into sets of existence of various heteroclinic networks is constructed.