Limit cycle bifurcations in a planar piecewise quadratic system with multiple parameters

Abstract

Abstract This paper is concerned with the number of limit cycles bifurcating from a period annulus for some planar piecewise smooth non-Hamiltonian systems. We construct a planar piecewise quadratic system with multiple parameters, obtain its lower bound for the maximum number of limit cycles by using Melnikov function method, and find more limit cycles than (Li and Liu in J. Math. Anal. Appl. 428:1354–1367, 2015).

Keywords

• Piecewise smooth system
• Melnikov function method
• Limit cycle