Analysis, synchronization and circuit design of a novel butterfly attractor

In this research work, a six-term 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel jerk system are obtained as L1 = 0.07765,L2 = 0, and L3 = −0.87912. The Kaplan-Yorke dimension of the novel jerk system is obtained as DKY = 2.08833. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model.

/pdf/adaptive-backstepping-control-synchronization-and-circuit-45iw8tvhw9.pdf

Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities

Hybrid phase synchronization is a new type of synchronization of a pair of chaotic systems called the master and slave systems. In hybrid phase synchronization, the odd numbered states of the master and slave systems are completely synchronized (CS), while their even numbered states are anti-synchronized (AS). The hybrid phase synchronization has applications in secure communications and cryptosystems. This work derives a new result for the hybrid phase synchronization of identical chaotic systems using sliding mode control. The main result has been proved using Lyapunov stability theory. Sliding mode control (SMC) is well-known as a robust approach and useful for controller design in systems with parameter uncertainties. As an application of this general result, a sliding mode controller is derived for the hybrid phase synchronization of the identical 3-D Vaidyanathan chaotic systems (2014). MATLAB simulations have been provided to illustrate the Vaidyanathan system and the hybrid synchronizer results for the identical Vaidyanathan systems.

Hybrid Synchronization of Identical Chaotic Systems Using Sliding Mode Control and an Application to Vaidyanathan Chaotic Systems

First, this paper announces a seven-term novel 3-D conservative chaotic system with four quadratic nonlinearities. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. An important property of the proposed novel chaotic system is that it has no equilibrium point. Hence, it displays hidden chaotic attractors. The Lyapunov exponents of the novel conservative chaotic system are obtained as L1 = 0.0395,L2 = 0 and L3 =−0.0395. The Kaplan-Yorke dimension of the novel conservative chaotic system is DKY = 3. Next, an adaptive controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical conservative chaotic systems with unknown parameters. MATLAB simulations have been depicted to illustrate the phase portraits of the novel conservative chaotic system and also the adaptive control results.

/pdf/analysis-and-adaptive-control-of-a-novel-3-d-conservative-no-56lhlghlzo.pdf

Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system

Memristor-based systems and their potential applications, in which memristor is both a nonlinear element and a memory element, have been received significant attention recently. A memristor-based hyperchaotic system with hidden attractor is studied in this paper. The dynamics properties of this hyperchaotic system are discovered through equilibria, Lyapunov exponents, bifurcation diagram, Poincaré map and limit cycles. In addition, its anti-synchronization scheme via adaptive control method is also designed and MATLAB simulations are shown. Finally, an electronic circuit emulating the memristor-based hyperchaotic system has been designed using off-the-shelf components.

/pdf/a-memristor-based-hyperchaotic-system-with-hidden-attractors-22a0x570td.pdf

A Memristor-Based Hyperchaotic System with Hidden Attractors: Dynamics, Synchronization and Circuital Emulating

In this paper, global chaos synchronization is investigated for n-scroll Chua (Tang et al. in IEEE Trans Circ Syst I Fundam Theory Appl 48:1369–1372, 2001) and Lur’e (Suykens and Vandewalle in Int J Bifurc Chaos 7:1323–1325, 1997) chaotic systems using backstepping control with recursive feedback. Our theorems on synchronization for n-scroll Chua and Lur’e chaotic systems are established using Lyapunov stability theory. The backstepping scheme is a recursive procedure that links the choice of Lyapunov function with the design of a feedback controller and guarantees global stability performance of strict-feedback chaotic systems. Mainly the backstepping technique gives flexibility in designing a feedback control law. Numerical simulations are also given to illustrate and validate the synchronization results derived in this paper.

Global Chaos Synchronization of n-Scroll Chua Circuit and Lur’e System using Backstepping Control Design with Recursive Feedback

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.

/pdf/global-chaos-synchronization-of-windmi-and-coullet-chaotic-43muzgnaio.pdf

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

This paper investigates the backstepping control design with novel feedback input approach for controlling chaotic systems to guarantee the complete synchronization as well as the anti-synchronization of chaotic systems, viz. n–scroll Chua (K. Wallace et.al. 2001) and Lur’e chaotic systems. Our theorems on hybrid synchronization for n–scroll Chua and Lur’e (J.Suyken et.al. 1997) chaotic systems is established using Lyapunov stability theory. Based on the Lyapunov function, the backstepping control is determined to tune the controller gain based on the precalculated feedback control inputs. The backstepping scheme is recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global stability performance of strict-feedback chaotic systems. Since the Lyapunov exponents are not required for these calculations, the backstepping control method is effective and convenient to synchronize the chaotic systems. Mainly this technique gives the flexibility to construct a control law. Numerical simulations are also given to illustrate and validate the hybrid synchronization results derived in this paper.

http://cejsh.icm.edu.pl/cejsh/element/bwmeta1.element.oai-journals-pan-pl-84246/c/oai-journals-pan-pl-84246_full-text_6.pdf

Hybrid synchronization of n–scroll Chua and Lur’e chaotic systems via backstepping control with novel feedback

In this paper, the hybrid synchronization is investigated for n-scroll chaotic Chua circuit (Wallace et al. (2001)) using adaptive backstepping control design based on recursive feedback control. Our theorems on hybrid synchronization for n-scroll chaotic Chua circuits are established using Lyapunov stability theory. 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 predetermined desired value. The adaptive backstepping control method is effective and convenient to synchronize and estimate the parameters of the chaotic systems. Mainly, this technique gives the flexibility to construct a control law and estimate the parameter values. Numerical simulations are also given to illustrate and validate the synchronization results derived in this paper.

/pdf/hybrid-synchronization-of-n-scroll-chaotic-chua-circuits-3nwr0094of.pdf

Hybrid Synchronization of n-scroll Chaotic Chua Circuits using Adaptive Backstepping Control Design with Recursive Feedback

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.

Suresh Rasappan

Papers

Global Chaos Synchronization of n-Scroll Chua Circuit and Lur’e System using Backstepping Control Design with Recursive Feedback

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

Hybrid synchronization of n–scroll Chua and Lur’e chaotic systems via backstepping control with novel feedback

Hybrid Synchronization of n-scroll Chaotic Chua Circuits using Adaptive Backstepping Control Design with Recursive Feedback

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