2009/10/31 by V. Resmi, G. Ambika, R. E. Amritkar
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaotic #Chaotic systems #Computer science #Computer simulation #Control theory (sociology) #Coupling (piping) #Engineering #Lorenz system #Lyapunov exponent #Lyapunov stability #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Phase (matter) #Phase plane #Phase synchronization #Physics #Plane (geometry) #Quantum chaos and dynamical systems #Quantum mechanics #Simulation #Stability (learning theory) #Statistical physics #Synchronization (alternating current) #Synchronization of chaos #Topology (electrical circuits) #nlin.CD
paper · pdf · doi:10.1103/physreve.81.046216
published as Phys Rev E 81, 046216 (2010) · 7 pages, 11 figures, appeared in Phys Rev E 81, 046216 (2010)
openalex publication_date 2010/04/29 · arxiv created 2010/05/04 · arxiv updated 2010/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider synchronization of chaotic systems coupled indirectly through common environment where the environment has an intrinsic dynamics of its own modulated via feedback from the systems. We find that a rich variety of synchronization behavior, such as in-phase, antiphase, complete, and antisynchronization, is possible. We present an approximate stability analysis for the different synchronization behaviors. The transitions to different states of synchronous behavior are analyzed in the parameter plane of coupling strengths by numerical studies for specific cases such as Rössler and Lorenz systems and are characterized using various indices such as correlation, average phase difference, and Lyapunov exponents. The threshold condition obtained from numerical analysis is found to agree with that from the stability analysis.