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Abstract In this work, we are interested in isolated crossing periodic orbits in planar piecewise polynomial vector fields defined in two zones separated by a straight line. In particular, in… Click to show full abstract
Abstract In this work, we are interested in isolated crossing periodic orbits in planar piecewise polynomial vector fields defined in two zones separated by a straight line. In particular, in the number of limit cycles of small amplitude. They are all nested and surrounding one equilibrium point or a sliding segment. We provide lower bounds for the local cyclicity for planar piecewise polynomial systems, M p c ( n ) , with degrees 2, 3, 4 , and 5. More concretely, M p c ( 2 ) ≥ 13 , M p c ( 3 ) ≥ 26 , M p c ( 4 ) ≥ 40 , and M p c ( 5 ) ≥ 58 . The computations use parallelization algorithms.
Journal Title: Nonlinear Analysis: Real World Applications
Year Published: 2021
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