Hybrid Chaos Synchronization of Four–Scroll Systems via Active Control

Abstract

This paper investigates the hybrid chaos synchronization of identical Wang four-scroll systems (Wang, 2009), identical Liu-Chen four-scroll systems (Liu and Chen, 2004) and non-identical Wang and Liu-Chen four-scroll systems. Active control method is the method adopted to achieve the hybrid chaos synchronization of the four-scroll chaotic systems addressed in this paper and our synchronization results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to hybrid synchronize identical and different Wang and Liu-Chen four-scroll chaotic systems. Numerical simulations are also shown to illustrate and validate the hybrid synchronization results derived in this paper.

Anti-synchronisation of identical chaotic systems via novel sliding control and its application to a novel chaotic system

“…Various control schemes have been developed to investigate the synchronisation and anti-synchronisation problems of the chaos literature such as active control method (Ho and Hung, 2002;Chen, 2005;Karthikeyan and Sundarapandian, 2014;Sarasu and Sundarapandian, 2011;Sundarapandian and Karthikeyan, 2012a;Vaidyanathan and Rajagopal, 2011;Zhang et al, 2012), adaptive control method (Abouelsoud and Mohamed, 2015;Liao and Tsai, 2000;Sundarapandian, 2012a, 2012b;Sundarapandian and Karthikeyan, 2011a, 2011b, 2012bVaidyanathan, 2012aVaidyanathan, , 2013cPakiriswamy, 2013, 2014;Vaidyanathan et al, 2014bVaidyanathan et al, , 2015d, backstepping method (Yu and Zhang, 2004;Park, 2006;Rasappan and Vaidyanathan, 2012a, 2012b, 2014Suresh and Sundarapandian, 2013;Vaidyanathan and Rasappan, 2014;Vaidyanathan et al, 2015f), sampled-data feedback control (Zhao and Lu, 2008), time-delay feedback method (Guo and Zhong, 2009), sliding mode control (Dhanalakshmi et al, 2015;Meng et al, 2014;Rhif, 2014;Shang and Wang, 2013;Sundarapandian and Sivaperumal, 2011;Vaidyanathan, 2012bVaidyanathan, , 2012cVaidyanathan and Sampath, 2012;Vaidyanathan et al, 2015g;…”

Analysis, Control, and Synchronization of a 3-D Novel Jerk Chaotic System with Two Quadratic Nonlinearities

“…Different types of synchronization such as complete synchronization [24], antisynchronization [45,55,46], hybrid synchronization [49,15], lag synchronization [31], phase synchronization [31,32], anti-phase synchronization [4], generalized synchronization [35], projective synchronization [21], generalized projective synchronization [36,37,65], etc. have been studied in the chaos literature.…”

Output Regulation of Vaidyanathan 3-D Jerk Chaotic System

“…The active control method [15,32,33,44,50,73,74,77] is typically used when the system parameters are available for measurement. Adaptive control method [34-36, 41-43, 54, 60, 67, 72, 75, 76, 81, 84] is typically used when some or all the system parameters are not available for measurement and estimates for the uncertain parameters of the systems.…”