Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperboli c Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters

By Sundarapandian Vaidyanathan. 2013

146 citations recorded by the source corpus.

This research work describes the modelling of two novel 3-D chaotic systems, the first with a hyperbolic sinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (A)) and the second with a hyperbolic cosinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (B)). In this work, a detailed qualitative analysis of the novel chaotic systems (A) and (B) has been presented, and the Lyapunov exponents and Kaplan-Yorke dimension of these chaotic systems have been obtained. It is found that the maximal Lyapunov exponent (MLE) for the novel chaotic systems (A) and (B) has a large value, viz. for the system (A) and for the system (B). Thus, both the novel chaotic systems (A) and (B) display strong chaotic behaviour. This research work also discusses the problem of finding adaptive controllers for the global chaos synchronization of identical chaotic systems (A), identical chaotic systems (B) and nonidentical chaotic systems (A) and (B) with unknown system parameters. The adaptive controllers for achieving global chaos synchronization of the novel chaotic systems (A) and (B) have been derived using adaptive control theory and Lyapunov stability theory. MATLAB simulations have been shown to illustrate the novel chaotic systems (A) and (B), and also the adaptive synchronization results derived for the novel chaotic systems (A) and (B).

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/142015156e7113ba8932f26c9c9c2a1fb5adbbd7

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In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

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.”
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.”
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.”