A survey on stably dissipative Lotka-Volterra systems with an application to infinite dimensional Volterra equations

Abstract

For stably dissipative Lotka-Volterra equations the dynamics on the attractor are Hamiltonian and we argue that complex dynamics can occur. We also present examples and properties of some infinite dimensional Volterra systems with applications related with stably dissipative Lotka-Volterra equations. We finish by mentioning recent contributions on the subject.