Abstract
This paper studies a fractional-order chaotic system with sine non-linearities and highlights its dynamics using the Lyapunov spectrum, bifurcation analysis, stagnation points, the solution of the system, the impact of the fractional order on the system, etc. The system considering uncertainties and disturbances was synchronized using dual penta-compound combination anti-synchronization among four master systems and twenty slave systems by non-linear control and the adaptive sliding mode technique. The estimates of the disturbances and uncertainties were also obtained using the sliding mode technique. The application of the achieved synchronization in secure communication is illustrated with the help of an example.
Highlights
Credit is due to Pecora and Carroll [13], who first performed complete synchronization between two chaotic systems in 1990 by designing controllers
The novel system considering uncertainties and disturbances was synchronized by introducing dual penta-compound combination antisynchronization among four master systems and twenty slave systems using different methods
Dual penta-compound combination anti-synchronization was performed on a chaotic system with two sine non-linearities
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Credit is due to Pecora and Carroll [13], who first performed complete synchronization between two chaotic systems in 1990 by designing controllers Many synchronization techniques such as double compound synchronization [14], difference synchronization [15], lag synchronization, phase synchronization [16], combination synchronization [17], parallel synchronization [18], dislocated synchronization [19], and fractional matrix and inverse fractional matrix synchronizations [20,21] have been developed since . The novel system considering uncertainties and disturbances was synchronized by introducing dual penta-compound combination antisynchronization among four master systems and twenty slave systems using different methods. Dual penta-compound combination anti-synchronization via non-linear control and adaptive sliding mode control and gives its proposed application.
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