Multiple Hopf bifurcations in coupled networks of planar systems

Abstract : In this communication, we study coupled networks built with non-identical instances of a dynamical system exhibiting a Hopf bifurcation. We first show how the coupling generates the birth of multiple limit cycles. Next, we project those coupled networks in the real plane, and construct a polynomial Hamiltonian system of degree n, admitting O(n 2) non-degenerate centers. We explore various perturbations of that Hamiltonian system and implement an algorithm for the symbolic computation of the Melnikov coefficients.