Nonlinear Control and Circuit Implementation in Coupled Nonidentical Fractional-Order Chaotic Systems

In this paper, circuit implementation and anti-synchronization are studied in coupled nonidentical fractional-order chaotic systems where a fractance module is introduced to approximate the fractional derivative. Based on the open-plus-closed-loop control, a nonlinear coupling strategy is designed to realize the anti-synchronization in the fractional-order Rucklidge chaotic systems and proved by the stability theory of fractional-order differential equations. In addition, using the frequency-domain approximation and circuit theory in the Laplace domain, the corresponding electronic circuit experiments are performed for both uncoupled and coupled fractional-order Rucklidge systems. Finally, our circuit implementation including the fractance module may provide an effective method for generating chaotic encrypted signals, which could be applied to secure communication and data encryption.

Automated summary

This paper investigates circuit implementation and anti-synchronization in coupled nonidentical fractional-order chaotic systems. A fractance module is introduced to approximate the fractional derivative. A nonlinear coupling strategy is designed and proved by stability theory to achieve anti-synchronization in the fractional-order Rucklidge chaotic systems. Circuit experiments are conducted to validate the theoretical results and suggest potential applications in secure communication and data encryption.