Adaptive Controller Design for the Hybrid Synchronization of Hyperchaotic XU and Hyperchaotic LI Systems

摘要

This paper derives new adaptive results for the hybrid synchronization of hyperchaotic Xi systems (2009)and hyperchaotic Li systems (2005).In thehybrid synchronizationdesignofmaster and slave systems,onepart of the systems, viz. their odd states, are completely synchronized (CS), while the other part, viz. theireven states, are completely anti-synchronized (AS) so that CS and AS co-exist in the process ofsynchronization.The research problem gets even more complicated, when the parameters of thehyperchaotic systems are unknown and we tackle this problem using adaptive control.The main results ofthis research workareproved using adaptive control theory andLyapunov stability theory.MATLABsimulationsusing classical fourth-order Runge-Kutta methodareshownforthe new adaptive hybridsynchronization results for thehyperchaoticXu andhyperchaoticLi systems