Journal
JOURNAL OF VIBRATION AND CONTROL
Volume 17, Issue 4, Pages 493-504Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1077546309357024
Keywords
Active control; chaos synchronization; F-6 Van der Pol and Duffing oscillators; Lyapunov stability theory; Routh-Hurwitz criteria; secure communications
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In this paper active controllers based on the Lyapunov stability theory and the Routh-Hurwitz criteria, are designed to completely synchronize two parametrically and externally excited Phi(6) Van der Pol oscillators, Phi(6) Duffing oscillators, and a Phi(6) Van der Pol oscillator with a Phi(6) Duffing oscillator in the triple-well configuration of the Phi(6) potential. The coefficient matrix of the error dynamics between each pair of synchronized systems is chosen such that the number of active control functions reduces from two to one, thereby significantly reducing controller complexity in the design. The designed controllers enable the state variables of the response system to synchronize with those of the master system in both the identical and nonidentical cases. The results are validated using numerical simulations. Application to secure communications is computationally demonstrated.
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