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Global organization of spiral structures in biparameter space of dissipative systems with Shilnikov saddle-foci

Roberto Barrio, Fernando Blesa, Sergio Serrano, and Andrey Shilnikov
Phys. Rev. E 84, 035201(R) – Published 19 September 2011

Abstract

We reveal and give a theoretical explanation for spiral-like structures of periodicity hubs in the biparameter space of a generic dissipative system. We show that organizing centers for “shrimp”-shaped connection regions in the spiral structure are due to the existence of Shilnikov homoclinics near a codimension-2 bifurcation of saddle-foci.

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  • Received 17 March 2011

DOI:https://doi.org/10.1103/PhysRevE.84.035201

©2011 American Physical Society

Authors & Affiliations

Roberto Barrio1,*, Fernando Blesa2, Sergio Serrano1, and Andrey Shilnikov3

  • 1Departamento de Matemática Aplicada and IUMA, University of Zaragoza, E-50009, Spain
  • 2Departamento de Física Aplicada, University of Zaragoza, E-50009, Spain
  • 3Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia, 30303, USA

  • *Corresponding author: rbarrio@unizar.es

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Vol. 84, Iss. 3 — September 2011

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