Synchronization With Positive Conditional Lyapunov Exponents
Changsong Zhou, C.-H. Lai
TL;DR
This paper investigates the conditions for synchronization in chaotic systems, emphasizing that positive conditional Lyapunov exponents can lead to synchronization due to computational effects and system contraction regions.
Contribution
It clarifies the role of positive conditional Lyapunov exponents in synchronization, challenging previous assumptions and highlighting the influence of finite precision in simulations.
Findings
Synchronization can occur with positive conditional Lyapunov exponents due to computational effects.
The contracting region of the system influences synchronization behavior.
Finite precision in simulations affects the observed synchronization phenomena.
Abstract
Synchronization of chaotic system may occur only when the largest conditional Lyapunov exponent of the driven system is negative. The synchronization with positive conditional Lyapunov reported in a recent paper (Phys. Rev. E, {\bf 56}, 2272 (1997)) is a combined result of the contracting region of the system and the finite precision in computer simulations.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Control and Stability of Dynamical Systems · Nonlinear Dynamics and Pattern Formation