Birth of limit cycles for a class of continuous and discontinuous differential systems in (d+2)-dimension

2015/01/08 by Jaume Llibre, Marco Antônio Teixeira, Llibre, J. +3
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1501.01987

openalex publication_date 2015/01/08 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

The orbits of the reversible differential system x=-y, y=x, z=0, with x,y ∈ R and z∈ R^d, are periodic with the exception of the equilibrium points (0,0, z). We compute the maximum number of limit cycles which bifurcate from the periodic orbits of the system x=-y, y=x, z=0, using the averaging theory of first order, when this system is perturbed, first inside the class of all polynomial differential systems of degree n, and second inside the class of all discontinuous piecewise polynomial differential systems of degree n with two pieces, one in y> 0 and the other in y<0. In the first case this maximum number is n^d(n-1)/2, and in the second is n^d+1.

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