Limit cycle bifurcations near a generalized homoclinic loop in piecewise smooth systems with a hyperbolic saddle on a switch line

作者：Wei, Lijun; Liang, Feng^*; Lu, Shiping

来源：Applied Mathematics and Computation, 2014, 243: 298-310.

DOI：10.1016/j.amc.2014.05.041

• Melnikov function
• Limit cycle bifurcation
• Generalized homoclinic loop
• Piecewise smooth system
• Near-Hamiltonian system

In this paper, we suppose a planar piecewise Hamiltonian system has a generalized homoclinic loop with a hyperbolic saddle on a switch line, and assume that there are two families of periodic orbits on both sides of the loop. Under perturbations we first give the expansion of the first Melnikov function near the loop. Then by using the first coefficients in the expansion, we study the number of limit cycles bifurcating from the homoclinic loop.

• 出版日期2014-9-15
• 单位安徽师范大学