Limit Cycles Bifurcating From A Zero-Hopf Type Equilibrium For Certain Autonomous Differential Systems

Abstract

The objective of this work is to study the existence of bifurcations of zero-Hopf type at the so-called Chen–Wang differential system y x y            z z  , , y  x 2  xz  3 y 2  a . The main tool up to now for studying a zero-Hopf bifurcation is to pass the system to the normal form of a zero-Hopf bifurcation. Our analysis of the zero-Hopf bifurcation is different; we study them directly using the averaging theory. In the second part of this work, we study the existence of zero-Hopf bifurcations of a Lorenz-Haken system in 4 R the averaging theory.