Unidirectional and Bidirectional Coupling Combination Synchronization of Double-Well Duffing Oscillators and Van der Pol Duffing Oscillators Using Linear State Feedback Control Techniques

Abstract

This paper investigates the synchronization of complex dynamical systems, specifically Double-Well Duffing Oscillators and Van der Pol Duffing Oscillators, using unidirectional and bidirectional coupling with linear state feedback control techniques. These oscillators exhibit nonlinear behavior that is widely relevant in engineering and physics, and their coupling mechanisms play crucial roles in applications like signal processing, secure communications, and mechanical systems. In this work, linear state feedback control was employed. The synchronization behavior under both unidirectional and bidirectional coupling schemes was examined. The system was observed by analyzing the stability, convergence rate, and effectiveness of the coupling. MATLAB software was used to validate the feasibility and effectiveness of the linear feedback coupling technique. The results demonstrate that combination synchronization can be achieved through the application of linear state error feedback control techniques in either unidirectional coupling or bidirectional coupling.