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).
Highlights
In the last decades, the study of piecewise smooth systems has attracted great interest for their wider range of application in modeling real phenomena [2, 3]
Quite a few methods and interesting results have been obtained on limit cycle bifurcations of piecewise smooth systems
The authors in [8] studied the maximum number of limit cycles which can bifurcate from the periodic orbits of the quadratic isochronous centers perturbed inside discontinuous quadratic polynomial differential systems
Summary
The study of piecewise smooth systems has attracted great interest for their wider range of application in modeling real phenomena [2, 3]. Quite a few methods and interesting results have been obtained on limit cycle bifurcations of piecewise smooth systems. The authors in [8] studied the maximum number of limit cycles which can bifurcate from the periodic orbits of the quadratic isochronous centers perturbed inside discontinuous quadratic polynomial differential systems. In [15], an expression of the first order Melnikov function is derived to study the number of limit cycles bifurcated from the periodic orbits of piecewise Hamiltonian systems. Of limit cycles which bifurcate from any compact region of the period annulus of system (1.3) for all possible bounded coefficients p±ij and qi±j independent of the small parameter ε up to the first order averaging method, and proved the following results:.
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