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- Title
STABILITY OF THE CONTROLLED SYNCHRONIZATION MANIFOLD IN A RING OF MUTUALLY COUPLED CHAOTIC SYSTEMS.
- Authors
YAMAPI, R.; AZIZ-ALAOUI, M. A.
- Abstract
The active control of the unstable synchronization manifold in a shift-invariant ring of N mutually coupled chaotic oscillators is investigated. After deriving the bifurcation structures and chaotic states in the single oscillator, we find the regime of coupling parameters leading to stable and unstable synchronization phenomena in the ring, using the Master stability function approach with the transverse Lyapunov exponents. The active control technique is applied on the mutually coupled chaotic systems to suppress unstable synchronization states. We derive the range of control gain parameters which leads to a successful control and the stability of the control design. The effects of the amplitude of the parametric perturbations on the stability boundaries of the controlled unstable synchronization process are also studied.
- Subjects
SYNCHRONIZATION; MANIFOLDS (Mathematics); CHAOS theory; DIFFERENTIABLE dynamical systems; NONLINEAR theories; CONTROL theory (Engineering); NONLINEAR oscillators; BIFURCATION theory
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2008, Vol 18, Issue 8, p2397
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127408021774