Synchronization in Coupled and Free Chaotic Systems
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.
KeywordsChaotic System Noise Intensity Unstable Manifold Stochastic Resonance Phase Synchronization
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