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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.
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Dates and versions

hal-01636245 , version 1 (16-11-2017)

Identifiers

  • HAL Id : hal-01636245 , version 1

Cite

Guillaume Cantin, M A Aziz-Alaoui, Nathalie Verdière, Valentina Lanza. Multiple Hopf bifurcations in coupled networks of planar systems. WANCSA 2017, Jul 2017, LE HAVRE, France. ⟨hal-01636245⟩
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