Abstract
The conditional Lyapunov exponent is defined for investigating chaotic synchronization, in particular complete synchronization and generalized synchronization. We find that the conditional Lyapunov exponent is expressed as a formula in terms of ergodic theory. Dealing with this formula, we find what factors characterize the conditional Lyapunov exponent in chaotic systems.
Highlights
The conditional Lyapunov exponent is defined for investigating chaotic synchronization [1,2,3,4,5,6,7,8,9,10,11,12,13,14], in particular Complete synchronization (CS) and Generalized synchronization (GS)
Existing research offered some mechanisms of chaotic synchronizations by focusing on mean amplitudes or variances of common input signals ( See [12, 13] for example), we find that such mean amplitudes or variances of common input signals are not imperative
In Appendix A, we summarize a short introduction of ergodic theory
Summary
The conditional Lyapunov exponent is defined for investigating chaotic synchronization [1,2,3,4,5,6,7,8,9,10,11,12,13,14], in particular Complete synchronization (CS) and Generalized synchronization (GS). It is widely known that the chaotic synchronization occurs in many systems, it is not clearly known why the conditional Lyapunov exponent changes. It has not completely been clarified why the CS occurs in chaotic systems. A report [10] showed that an external forcing input in CS may change the dynamical system to another one. The explanation is well considered, there could be another reason why the conditional Lyapunov exponent may change They have focused on the mean of external forcing inputs for the CS. In Appendix A, we summarize a short introduction of ergodic theory
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