Synchronization in Coupled and Free Chaotic Systems

  • F. T. Arecchi
  • R. Meucci
  • E. Allaria
  • S. Boccaletti
Part of the New Economic Windows book series (NEW)


Global bifurcations in dynamical systems are of considerable interest because they can lead to the creation of chaotic behaviour [Hilborn, 1994]. Global bifurcations are to be distinguished from local bifurcations around an unstable periodic solution. Typically, they occur when a homoclinic point is created. A homoclinic point is an intersection point between the stable and the unstable manifold of a steady state saddle point p on the Poincaré section of a, at least, 3D flow. The presence of a homoclinic point implies a complicated geometrical structure of both the stable and the unstable manifolds usally referred to as a homoclinic tangle. When a homoclinic tangle has developed, a trajfectory that comes close to the saddle point behaves in an erratic way, showing sensitivity to initial conditions.


Chaotic System Noise Intensity Unstable Manifold Stochastic Resonance Phase Synchronization 
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Copyright information

© Springer-Verlag Italia 2007

Authors and Affiliations

  • F. T. Arecchi
    • 1
  • R. Meucci
    • 1
  • E. Allaria
    • 1
  • S. Boccaletti
    • 1
  1. 1.Dept. of PhysicsUniv. of Firenze INOAItaly

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