Bifurcating limit cycles in quadratic polynomial differential systems

Abstract

We conducted a study on the plane quadratic polynomial differential systems with two or three parameters. Bifurcation curves were drawn in the cross-section of parameter space, dividing the section into several regions. Different number of limit cycles can be identified in different regions. Diagrams of variation of amplitude of limit cycles versus parameters are shown and realistic examples of systems having different number of limit cycles are constructed. As an example, a quadratic equation with limit cycles in (1,3) distribution is shown.