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

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  • Liu, Shanshan
  • Han, Maoan

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.

Suggested Citation

  • Liu, Shanshan & Han, Maoan, 2023. "Limit cycle bifurcations near double homoclinic and double heteroclinic loops in piecewise smooth systems," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008718
    DOI: 10.1016/j.chaos.2023.113970
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