Analysis and Anti-Synchronization of a Novel Chaotic System via Active and Adaptive Controllers

By V. Sundarapandian. 2013

143 citations recorded by the source corpus.

Anti-synchronization of chaotic systems deals with the problem of asymptotically synchronizing the sum of states of a pair of chaotic systems called master and slave systems with the help of controllers attached to the slave system. When two chaotic systems are anti-synchronized, then their states are asymptotically equal in magnitude, but opposite in phase. Anti-synchronization of chaotic systems has applications in many engineering areas such as secure communications, secure data encryption, cryptosystems, etc. This paper announces a novel 3-D chaotic system and describes its qualitative properties. Next, this paper deals with the design of active and adaptive controllers for synchronizing the states of identical novel chaotic systems. Active controllers are used when the system parameters are available for measurement and the synchronization result is established using Lyapunov stability theory. Adaptive controllers are used when the system parameters are unknown. In this case, estimates are used in lieu of the unknown system parameters and adaptive controllers are designed using adaptive control theory and Lyapunov stability theory. Numerical simulations using MATLAB have been shown to demonstrate the proposed active and adaptive synchronization results for novel chaotic systems.

Subfields: Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/370141c603cba81c935edcac6d05f64f81f34b06

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In Computer Vision and Pattern Recognition

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.”
Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities (2014, background): “Many new chaotic systems have been also discovered like Li system [52], Sundarapandian system [53], Vaidyanathan systems [54, 55, 56, 57], Vaidyanathan-Madhavan system [58], Sundarapandian-Pehlivan system [59], PehlivanMoroz-Vaidyanathan system [60], Jafari system [61], Pham system [62], etc.”
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.”
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.”