Hybrid Chaos Synchronization of Hyperchaotic LIU And Hyperchaotic CHEN Systems by Active Nonlinear Control

Abstract

This paper investigates the hybrid chaos synchronization of identical 4-D hyperchaotic Liu systems (2006), 4-D identical hyperchaotic Chen systems (2005) and hybrid synchronization of 4-D hyperchaoticLiu and hyperchaotic Chen systems. The hyperchaotic Liu system (Wang and Liu, 2005) and hyperchaotic Chen system (Li, Tang and Chen, 2006)

Projective synchronization for a new class of chaotic/hyperchaotic systems with and without parametric uncertainty

“…Numerous control procedures have been established for chaos synchronization of chaotic/hyperchaotic systems. For example, observer-based control (Mohammadpour and Binazadeh, 2018), adaptive control (Ahmad and Shafiq, 2020; Wu et al, 2008), backstepping control (Vincent, 2008), active control (Pallav and Handa, 2021; Park, 2006; Vaidyanathan, 2011), sliding mode control (Chen et al, 2012; Shahi and Fallah Kazemi, 2017), feedback control (Pallav and Handa, 2022), and so on. Several synchronization schemes such as hybrid synchronization (Singh et al, 2014a), generalized synchronization (Wang and Guan, 2006), complete synchronization (Fabiny and Wiesenfeld, 1991), anti-synchronization (Mossa Al-sawalha and Noorani, 2009), hybrid projective synchronization (HPS; Mainieri and Rehacek, 1999; Wei et al, 2014), projective synchronization (Li, 2007), and so on have also been introduced and are gaining popularity with time.…”

Adaptive Control for the Stabilization and Synchronization of Nonlinear Gyroscopes

“…Similarly, the experimental design of nonlinear control inputs such as proposed in [25,[28][29][30][31][32] are very difficult, due to the complexity of the control functions, especially when the system parameters are unknown due to inevitable perturbation by external inartificial factors. Although in [30][31][32][33][34] the sliding mode control was proposed that could be applicable to the above situations in the presence of parameter uncertainty [31]; however there were many assumptions to be made in the construction of the controllers. For example, in [30] the exact values of the functions are unknown due to parameter uncertainty; some upper bounds of uncertainties are necessary and also assumed that all the state variables of the master and slave systems are available for control design.…”