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Limit cycles of planar picewise linear Hamiltonian systems without equilibrium points separated by two circles

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Abstract

Because of their applications to many physical phenomena in recent decades, interest in the study of piecewise discontinuous differential systems has increased greatly. Limit cycles play an important role in the study of any planar differential system, but determining the maximum number of limit cycles that a class of planar differential systems can have is one of the main problems in the qualitative theory of planar differential systems. Thus, in general, providing a precise upper bound for the number of crossing limit cycles that a given class of piecewise linear differential systems can have is a very difficult problem. In this paper, we provide the exact upper bound of limit cycles for linear piecewise differential systems, formed by linear Hamiltonian systems without equilibrium and separated by a two concentric circles. Furthermore, we prove that our result is reached by giving some systems having exactly one, two or three limit cycles.

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  1. Department of Mathematics, University Mohamed El Bachir El Ibrahimi of Bordj Bou Arréridj, 34000, El Anasser, Algeria

    Loubna Damene & Rebiha Benterki

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  1. Loubna Damene
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  2. Rebiha Benterki
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Correspondence to Rebiha Benterki.

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Damene, L., Benterki, R. Limit cycles of planar picewise linear Hamiltonian systems without equilibrium points separated by two circles. Rend. Circ. Mat. Palermo, II. Ser 72, 1103–1114 (2023). https://doi.org/10.1007/s12215-021-00716-5

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  • DOI: https://doi.org/10.1007/s12215-021-00716-5

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