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

By Sundarapandian Vaidyanathan, Christos K. Volos, Viet-Thanh Pham, K. Madhavan, Babatunde A. Idowu. 2014

165 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fe51ab5e0ea06f4d32f63fc47e78def79686c207

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In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

Adaptive Chaotic Synchronization of Enzymes-Substrates System with Ferroelectric Behaviour in Brain Waves (2015, background): “Many new chaotic systems have been also discovered in the recent years like Sundarapandian systems [11, 12], Vaidyanathan systems [13-37], Pehlivan system [38], Pham system [39], etc.”
A Memristor-Based Hyperchaotic System with Hidden Attractors: Dynamics, Synchronization and Circuital Emulating (2015, methodology): “Lorenz system [31], Rössler system [32], Chen system [33], Sprott system [34], Sundarapandian systems [35-36], Vaidyanathan systems [37-44], Pehlivan system [45], etc., belong to the class of chaotic systems with self-excited attractors.”
Global Chaos Synchronization of Chemical Chaotic Reactors via Novel Sliding Mode Control Method (2015, background): “Many new chaotic systems have been also discovered in the recent years like Sundarapandian systems [11, 12], Vaidyanathan systems [13-42], Pehlivan system [43], Pham system [44], etc.”
A 3 - D Novel Conservative Chaotic System and its Generalized Projective Synchronization via Adaptive Control (2015, background): “We note that the chaotic systems [2-34] are dissipative systems in which the system limit sets are ultimately confined into a specific limit set of zero volume, and the asymptotic motion of the chaotic system settles onto a strange attractor of the system.”