Limit cycle bifurcations for piecewise smooth integrable differential systems
Jihua Yang Liqin Zhao
Discrete & Continuous Dynamical Systems - B 2017, 22(6): 2417-2425 doi: 10.3934/dcdsb.2017123

In this paper, we study a class of piecewise smooth integrable non-Hamiltonian systems, which has a center. By using the first order Melnikov function, we give an exact number of limit cycles which bifurcate from the above periodic annulus under the polynomial perturbation of degree n.

keywords: Integrable differential system limit cycle Melnikov function
Limit cycle bifurcations of a piecewise smooth Hamiltonian system with a generalized heteroclinic loop through a cusp
Jihua Yang Erli Zhang Mei Liu
Communications on Pure & Applied Analysis 2017, 16(6): 2321-2336 doi: 10.3934/cpaa.2017114

In this paper we study the limit cycle bifurcation of a piecewise smooth Hamiltonian system. By using the Melnikov function of piecewise smooth near-Hamiltonian systems, we obtain that at most $12n+7$ limit cycles can bifurcate from the period annulus up to the first order in $\varepsilon$.

keywords: Piecewise smooth Hamiltonian system generalized heteroclinic loop Melnikov function cusp

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