Bifurcation of limit cycles in piecewise holomorphic systems separated by two external circles
Abstract
The study examines limit cycle bifurcations from linear centers perturbed by three-zone piecewise holomorphic systems separated by external circles, identifying configurations that yield at least sixteen limit cycles in fourth-degree systems.
This work investigates the number of limit cycles bifurcating from the periodic orbits of a linear center when it is perturbed by piecewise holomorphic systems with three zones separated by two external circles. We analyze how different geometric configurations of these zones influence the number of limit cycles. Moreover, we show the existence of at least sixteen limit cycles in fourth-degree piecewise polynomial holomorphic systems under certain configurations.
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