Melnikov functions and limit cycle bifurcations for a class of piecewise Hamiltonian systems

Abstract

This study evaluated the number of limit cycles for a class of piecewise Hamiltonian systems with two zones separated by two semi-straight lines. First, we obtained explicit expressions of higher Melnikov functions. Then we applied these expressions to find the upper bounds of the number of limit cycles bifurcated from a period annulus of a piecewise polynomial Hamiltonian system.

Keywords

• piecewise smooth system
• melnikov function
• limit cycle
• bifurcation