Global chaos synchronization of a four-scroll novel chaotic system via novel sliding mode control

Vaidyanathan, Sundarapandian; Sampath, Sivaperumal

doi:10.1109/icsemr.2014.7043682

Cited by 13 publications

(19 citation statements)

References 56 publications

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“…Synchronization of chaotic systems is a phenomenon that occurs when two or more chaotic systems are coupled or when a chaotic system drives another chaotic system [36,51,61].…”

Section: Introductionmentioning

confidence: 99%

Backstepping Controller Design for the Global Chaos Synchronization of Sprott’s Jerk Systems

Vaidyanathan

Idowu

Azar

2014

Chaos Modeling and Control Systems Design

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113

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This research work investigates the global chaos synchronization of Sprott's jerk chaotic system using backstepping control method. Sprott's jerk system (1997) is algebraically the simplest dissipative chaotic system consisting of five terms and a quadratic nonlinearity. Sprott's chaotic system involves only five terms and one quadratic nonlinearity, while Rössler's chaotic system (1976) involves seven terms and one quadratic nonlinearity. This work first details the properties of the Sprott's jerk chaotic system. The phase portraits of the Sprott's jerk system are described. The Lyapunov exponents of the Sprott's jerk system are obtained as L 1 = 0.0525, L 2 = 0 and L 3 = −2.0727. The Lyapunov dimension of the Sprott's jerk system is obtained as D L = 2.0253. Next, an active backstepping controller is designed for the global chaos synchronization of identical Sprott's jerk systems with known parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict-feedback chaotic systems. Finally, an adaptive backstepping controller is designed for the global chaos synchronization of identical Sprott's jerk systems with unknown parameters. MATLAB simulations are provided to validate and demonstrate the effectiveness of the proposed active and adaptive chaos synchronization schemes for the Sprott's jerk systems.

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“…Synchronization of chaotic systems is a phenomenon that occurs when two or more chaotic systems are coupled or when a chaotic system drives another chaotic system [36,51,61].…”

Section: Introductionmentioning

confidence: 99%

Backstepping Controller Design for the Global Chaos Synchronization of Sprott’s Jerk Systems

Vaidyanathan

Idowu

Azar

2014

Chaos Modeling and Control Systems Design

Self Cite

113

View full text Add to dashboard Cite

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“…Chaos theory deals with nonlinear dynamical systems that are very sensitive to even small changes in the initial conditions, known as chaotic systems ([1]- [2]). Chaos theory has applications in several areas of science and engineering such as plasma systems [3], weather systems ( [4]- [5]), chemical reactions ( [6]- [8]), ecology ([9]- [10]), biology ( [11]- [14]), encryption ( [15]- [18]), robotics [19], neural networks ( [20]- [21]), oscillations ( [22]- [29]), circuits ( [30]- [41]), etc. Gottlieb [42] established that 3-D chaotic systems can be expressed in the form of single ordinary differential equations, which are also termed as jerk differential equations.…”

Section: Introductionmentioning

confidence: 99%

A New Chaotic Jerk System with Three Nonlinearities and Synchronization via Adaptive Backstepping Control

Vaidyanathan¹,

Kingni²,

Sambas³

et al. 2018

IJET

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Jerk systems are popular in mechanical engineering and chaotic jerk systems are used in many applications as they have simple structure and complex dynamic properties. In this work, we report a new chaotic jerk system with three nonlinear terms. Dynamical properties of the chaotic jerk system are analyzed through equilibrium analysis, dissipativity, phase portraits and Lyapunov chaos exponents. We show that the new chaotic jerk system has a unique saddle-focus equilibrium at the origin. Thus, the new chaotic jerk system has a self-excited strange attractor. Next, global chaos synchronization of a pair of new chaotic jerk systems is successfully achieved via adaptive backstepping control.

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“…It is well-known that chaos theory has application has many branches of science and engineering ([1]- [2]). Some popular applications can be mentioned as plasma systems [3], weather systems ( [4]- [5]), chemical reactions ( [6]- [8]), encryption ([9]- [12]), robotics [13], oscillations ([14]- [17]), circuits ( [18]- [21]), etc. In 1996, it was shown by Gottlieb [22] that 3-D chaotic systems can be expressed in the form of single ordinary differential equations, which are also termed as jerk differential equations.…”

Section: Introductionmentioning

confidence: 99%

A New Hyperchaotic Hyperjerk System with Three Nonlinear Terms, its Synchronization and Circuit Simulation

Vaidyanathan

Sambas²,

Afendee

et al. 2018

IJET

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In recent decades, hyperjerk systems have been studied well in the literature because of their simple dynamics structure and complex qualitative properties. In this work, we announce a new hyperchaotic hyperjerk system with three nonlinear terms. Dynamical properties of the hyperjerk system are analyzed through equilibrium analysis, dissipativity, phase portraits and Lyapunov chaos exponents. We show that the new hyperchaotic hyperjerk system has a unique saddle-focus equilibrium at the origin. Thus, the new hyperchaotic hyperjerk system has a self-excited strange attractor. Next, global hyperchaos synchronization of a pair of new hyperchaotic hyperjerk systems is successfully achieved via adaptive backstepping control. Also, an electronic circuit of the hyperchaotic hyperjerk system has been designed via MultiSIM to check the feasibility of the theoretical system.

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Global chaos synchronization of a four-scroll novel chaotic system via novel sliding mode control

Cited by 13 publications

References 56 publications

Backstepping Controller Design for the Global Chaos Synchronization of Sprott’s Jerk Systems

Backstepping Controller Design for the Global Chaos Synchronization of Sprott’s Jerk Systems

A New Chaotic Jerk System with Three Nonlinearities and Synchronization via Adaptive Backstepping Control

A New Hyperchaotic Hyperjerk System with Three Nonlinear Terms, its Synchronization and Circuit Simulation

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