Targeting engineering synchronization in chaotic systems
Sourav K. Bhowmick, Dibakar Ghosh
TL;DR
This paper presents a linear feedback control method to achieve various synchronization states in chaotic systems, providing an analytical framework and numerical validation for targeted synchronization in mismatched and identical systems.
Contribution
It introduces a general coupling design based on Lyapunov stability theory for targeting any desired synchronization state in chaotic systems.
Findings
Successful control of mixed, linear, and nonlinear synchronization states
Analytical coupling design derived for unidirectional synchronization
Numerical validation on Lorenz and Sprott oscillators
Abstract
A method of targeting engineering synchronization states in two identical and mismatch chaotic systems is explained in details. The method is proposed using linear feedback controller coupling for engineering synchronization such as mixed synchronization, linear and nonlinear generalized synchronization and targeting fixed point. The general form of coupling design to target any desire synchronization state under unidirectional coupling with the help of Lyapunov function stability theory is derived analytically. A scaling factor is introduced in the coupling definition to smooth control without any loss of synchrony. Numerical results are done on two mismatch Lorenz systems and two identical Sprott oscillators.
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