On the limit cycles of perturbed discontinuous planar systems with 4 switching lines. (English) Zbl 1355.34036
Summary: Limit cycle bifurcations for a class of perturbed planar piecewise smooth systems with 4 switching lines are investigated. The expressions of the first order Melnikov function are established when the unperturbed system has a compound global center, a compound homoclinic loop, a compound 2-polycycle, a compound 3-polycycle or a compound 4-polycycle, respectively. Using Melnikov’s method, we obtain lower bounds of the maximal number of limit cycles for the above five different cases. Further, we derive upper bounds of the number of limit cycles for the later four different cases. Finally, we give a numerical example to verify the theory results.
MSC:
| 34A36 | Discontinuous ordinary differential equations |
| 34E10 | Perturbations, asymptotics of solutions to ordinary differential equations |
| 37G15 | Bifurcations of limit cycles and periodic orbits in dynamical systems |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 34C23 | Bifurcation theory for ordinary differential equations |
Keywords:
perturbed planar piecewise smooth system; Melnikov function; Poincaré map; limit cycle; bifurcationReferences:
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