3D Quadratic ODE systems with an infinite number of limit cycles

Abstract

We consider an autonomous three-dimensional quadratic ODE system with nine parameters, which is a generalization of the Langford system. We derive conditions under which this system has infinitely many limit cycles. First, we study the equilibrium points of such systems and their eigenvalues. Next, we prove the non-local existence of an infinite set of limit cycles emerging by means of Andronov – Hopf bifurcation.