Abstract
In the present work, Lyapunov stability theory, nonlinear adaptive control law and the parameter update law were utilized to derive the state of two new chaotic reversal systems after being synchronized by the function projective method. Using this technique allows for a scaling function instead of a constant thereby giving a better method in applications in secure communication. Numerical simulations are presented to demonstrate the effective nature of the proposed scheme of synchronization for the new chaotic reversal system.
Highlights
The chaotic dynamics observed only in nonlinear systems have been largely defined by oscillations which are sensitive to initial conditions [1]
The work of Pecora and Caroll [4] generated a wider research in synchronization since it entails the synchronization of two identical chaotic systems with different initial conditions.A number of methods of synchronization have been proposed since the pioneering work of Pecora and Caroll such as complete synchronization, generalized synchronization, phase synchronization, lag synchronization, adaptive synchronization, timescale synchronization, intermittent synchronization, projective synchronization and function projective synchronization [5]-[9]
Function projective synchronization of new chaotic reversal systems [10] with uncertain parameters using nonlinear adaptive controller has been investigated to demonstrate the effectiveness of this scheme as it applies in secure communication
Summary
The chaotic dynamics observed only in nonlinear systems have been largely defined by oscillations which are sensitive to initial conditions [1]. Lorenz and Rossler systems are pioneering simple chaotic systems discovered with a lot of interesting properties that can model physical systems [1]-[2] This relatively new dynamical behaviour has since been discovered in other disciplines such as engineering, science and economics. Function projective synchronization of new chaotic reversal systems [10] with uncertain parameters using nonlinear adaptive controller has been investigated to demonstrate the effectiveness of this scheme as it applies in secure communication. The remaining part of this work is arranged as follows: section 2 is on the nonlinear adaptive controller designed to synchronize the new chaotic reversal systems, section 3 is on numerical simulations presented to demonstrate the robust nature of the scheme, and section 4 is the conclusion of the paper
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