On the Number of Limit Cycles for Piecewise Polynomial Holomorphic Systems
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Society for Industrial & Applied Mathematics (SIAM)
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In this paper, we are concerned with determining lower bounds of the number of limit cycles for piecewise polynomial holomorphic systems with a straight line of discontinuity. We approach this problem with different points of view. Initially, we study the number of zeros of the first- and second-order averaging functions. We also use the Lyapunov quantities to produce limit cycles appearing from a monodromic equilibrium point via a degenerated Andronov-Hopf type bifurcation, adding at the very end the sliding effects. Finally, we use the Poincaré-Miranda theorem for obtaining an explicit piecewise linear holomorphic system with 3 limit cycles, a result that improves the known examples in the literature that had a single limit cycle.
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SIAM Journal on Applied Dynamical Systems, v. 23, n. 3, p. 2593-2622, 2024.
