Suresh Rasappan

Global Chaos Synchronization of WINDMI and Coullet Chaotic Systems using Adaptive Backstepping Control Design

In this paper, global chaos synchronization is investigated for WINDMI (J. C. Sprott, 2003) and Coullet (P. Coullet et al, 1979) chaotic systems using adaptive backstep- ping control design based on recursive feedback control. Our theorems on synchronization for WINDMI and Coullet chaotic systems are established using Lyapunov stability the- ory. The adaptive backstepping control links the choice of Lyapunov function with the design of a controller and guarantees global stability performance of strict-feedback chaotic systems. The adaptive backstepping control maintains the parameter vector at a predeter- mined desired value. The adaptive backstepping control method is efiective and convenient to synchronize and estimate the parameters of the chaotic systems. Mainly, this technique gives the ∞exibility to construct a control law and estimate the parameter values. Numeri- cal simulations are also given to illustrate and validate the synchronization results derived in this paper.

Global Chaos Synchronization of Hyperchaotic Bao and Xu Systems by Active Nonlinear Control

This paper investigates the global chaos synchronization of hyperchaotic systems, viz. synchronization of identical hyperchaotic Bao systems (Bao and Liu, 2008), and synchronization of non-identical hyperchaotic Bao and Xu systems. Active nonlinear feedback control is the method used to achieve the synchronization of the chaotic systems addressed in this paper. Our theorems on global chaos synchronization for hyperchaotic Bao and Xu systems 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 synchronize identical and different hyperchaotic Bao and Xu systems. Numerical simulations are also given to illustrate and validate the various synchronization results derived in this paper.This paper investigates the global chaos synchronization of hyperchaotic systems, viz. synchronization of identical hyperchaotic Bao systems (Bao and Liu, 2008), and synchronization of non-identical hyperchaotic Bao and Xu systems. Active nonlinear feedback control is the method used to achieve the synchronization of the chaotic systems addressed in this paper. Our theorems on global chaos synchronization for hyperchaotic Bao and Xu systems 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 synchronize identical and different hyperchaotic Bao and Xu systems. Numerical simulations are also given to illustrate and validate the various synchronization results derived in this paper.

Synchronization of Hyperchaotic Liu System via Backstepping Control with Recursive Feedback

This paper investigates the backstepping control design with recursive feedback input approach for achieving global chaos synchronization of identical hyperchaotic Liu systems(2001). Our theorem on global chaos synchronization for hyperchaotic Liu systems is established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the backstepping control method is effective and convenient to synchronize the hyperchaotic Liu systems. Numerical simulations are also given to illustrate the synchronization results derived in this paper.

Hybrid Synchronization of Hyperchaotic Qi and Lü Systems by Nonlinear Control

This paper investigates the hybrid synchronization of identical hyperbolic Qi systems and hybrid synchronization of hyperchaotic Qi and Lu systems. The hyperchaotic Qi system (2008) and hyperchaotic Lu system (2006) are important models of hyperchaotic systems. Hybrid synchronization of the hyperchaotic systems is achieved through synchronization of two pairs of states and anti-synchronization of the other two pairs of states of the two hyperchaotic systems. Nonlinear control is the method used for the hybrid synchronization of identical hyperbolic Qi systems and hybrid synchronization of hyperchaotic Qi and Lu systems. Since the Lyapunov exponents are not required for these calculations, this method is effective and convenient to achieve hybrid synchronization of the two hyperchaotic systems. Numerical simulations are shown to verify the results.

Hybrid Synchronization of Arneodo and Rössler Chaotic Systems by Active Nonlinear Control

This paper investigates the hybrid chaos synchronization of identical Arneodo systems (1981), identical Rossler systems (1976) and non-identical Arneodo and Rossler systems. In hybrid synchronization of chaotic systems, one part of the systems is synchronized and the other part is anti-synchronized so that complete synchronization (CS) and anti-synchronization (AS) co-exist in the systems. The co-existence of CS and AS is very useful in secure communication and chaotic encryption schemes. Active nonlinear control is the method used for the hybrid synchronization of the chaotic systems addressed in this paper. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to achieve hybrid synchronization of the two chaotic systems. Numerical simulations are shown to verify the results.

New Results on the Global Chaos Synchronization for Liu-Chen-Liu and Lü Chaotic Systems

This paper investigates the global chaos synchronization of two identical Liu-Chen-Liu chaotic systems (2007) and two different chaotic systems, namely, Liu-Chen-Liu chaotic system (2007) and Lu chaotic system (2002). Nonlinear control is an effective method for making two identical chaotic systems or two different chaotic systems synchronized. Since the Lyapunov exponents are not required for the calculations, this method is an effective and convenient to synchronize two identical and different chaotic systems. Numerical simulations are also given to validate the proposed synchronization approach.

Chaos synchronization of coplitts oscillator via backstepping control

This paper derives new results for the chaos synchronization of Colpitts oscillator (1994) via backstepping control method. Our main theorem on chaos synchronization for Colpitts oscillator has been proved using Lyapunov stability theory. The backstepping scheme is a recursive procedure that links the choice of a Lyapunov function with the design of a controller. The backstepping control method is effective and convenient to synchronize identical systems. Numerical simulations with MATLAB are also given to illustrate and validate the synchronization result derived in this paper.