Limit cycle bifurcations near double homoclinic and double heteroclinic loops in piecewise smooth systems

Shanshan Liu and Maoan Han

Chaos, Solitons & Fractals, 2023, vol. 175, issue P1

Abstract: In this paper, the number and distributions of limit cycles bifurcating from a double homoclinic loop and a double heteroclinic loop of piecewise smooth systems with three zones are considered. By introducing a suitable Poincaré map near the double homoclinic loop, three criteria are derived to judge its inner and outer stability. Then through stability-changing method, bifurcation theorems of limit cycles near the double homoclinic and double heteroclinic loops for non-symmetric and symmetric piecewise near-Hamiltonian systems are established. A piecewise linear Z2-equivariant system is presented as an application and five limit cycles are obtained, three of which are alien limit cycles.

Keywords: Piecewise smooth systems; Double homoclinic loop; Double heteroclinic loop; Stability; Limit cycle (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008718

DOI: 10.1016/j.chaos.2023.113970

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