Abstract
Generalized projective synchronization (GPS) of chaotic systems generalizes known types of synchronization schemes such as complete synchronization (CS), anti-synchronization (AS), hybrid synchronization (HS), projective synchronization (PS), etc. In this work, we have designed active and adaptive controllers for the generalized projective synchronization (GPS) of identical Vaidyanathan chaotic systems (2014). Vaidyanathan system is an eight-term chaotic system with three quadratic nonlinearities. The Lyapunov exponents of the Vaidyanathan chaotic system are obtained as \(L_1 = 6.5294, L_2 = 0\) and \(L_3 = -26.4696\). Since the maximal Lyapunov exponent of the Vaidyanathan system is \(L_1 = 6.5294\), the system exhibits highly chaotic behaviour. The Kaplan–Yorke dimension of the Vaidyanathan chaotic system is obtained as \(D_{KY} = 2.2467\). The main GPS results in this work have been established using Lyapunov stability theory. MATLAB plots have been depicted to illustrate the phase portraits of the Vaidyanathan chaotic system and also the GPS results for Vaidyanathan chaotic systems using active and adaptive controllers.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
