Limit cycle bifurcations by perturbing non-smooth Hamiltonian systems with 4 switching lines via multiple parameters

In this paper, we investigate the limit cycle bifurcation in perturbations of non-smooth Hamiltonian systems with 4 switching lines via multiple parameters. Using the first order Melnikov function, we derive some computational formulas, which can be used to study the bifurcation of limit cycles. As an application to the obtained results, we consider the limit cycle bifurcation problem of a non-smooth system studied in Wang and Han (2016). Comparing with the result in the above reference, we find n−1,n∈N+ more limit cycles by our method.