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Riddling, bubbling, and Hopf bifurcation in coupled map systems
1Department of Physics, University of Potsdam, Am Neuen Palais, Postfach 601553, D-14415 Potsdam, Germany.
Summary
Desynchronization in coupled chaotic systems occurs via Hopf bifurcations. This study reveals a novel Hopf bifurcation leading to blowout bifurcations in chaotic attractors.
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Dynamical systems
Background:
- Coupled map lattices exhibit complex behaviors.
- Understanding bifurcations is crucial for predicting system transitions.
- Chaotic attractors represent complex, unpredictable dynamics.
Purpose of the Study:
- To investigate the mechanism of desynchronization in a simple coupled-map system.
- To characterize a novel type of Hopf bifurcation leading to blowout bifurcations from chaotic attractors.
- To analyze the phenomena of riddling and bubbling associated with this bifurcation.
Main Methods:
- Analysis of a simple coupled-map system.
- Identification and study of Hopf bifurcations.
- Investigation of blowout bifurcations from chaotic attractors.
- Examination of riddling and bubbling phenomena.
Main Results:
- Desynchronization of the chaotic attractor is shown to occur through a series of Hopf bifurcations.
- A new type of Hopf bifurcation, leading to blowout bifurcation from a chaotic attractor, is identified.
- The characteristics of riddling and bubbling are analyzed in the context of this novel bifurcation.
Conclusions:
- Hopf bifurcations play a key role in the desynchronization of chaotic attractors in coupled systems.
- The identified Hopf bifurcation represents a new pathway to blowout bifurcations from chaos.
- Riddling and bubbling are important features of this specific type of bifurcation.