Qualitative Study and Adaptive Control of a Novel 4-D Hyperchaotic System with Three Quadratic Nonlinearities

2016 ◽  
pp. 179-202 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Ahmad Taher Azar
Keyword(s):  
Adaptive Control ◽  
Qualitative Study ◽  
Hyperchaotic System ◽  
Quadratic Nonlinearities

scholarly journals Hyperchaos, adaptive control and synchronization of a novel 4-D hyperchaotic system with two quadratic nonlinearities

2016 ◽  
Vol 26 (4) ◽  
pp. 471-495 ◽  
Author(s):  
Sundarapandian Vaidyanathan
Keyword(s):  
Adaptive Control ◽  
Lyapunov Exponents ◽  
Research Work ◽  
Adaptive Controller ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
The Novel ◽  
System Parameters ◽  
Quadratic Nonlinearities ◽  
Unknown System

AbstractThis research work announces an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. We describe the qualitative properties of the novel 4-D hyperchaotic system and illustrate their phase portraits. We show that the novel 4-D hyperchaotic system has two unstable equilibrium points. The novel 4-D hyperchaotic system has the Lyapunov exponents L1= 3.1575, L2= 0.3035, L3= 0 and L4= −33.4180. The Kaplan-Yorke dimension of this novel hyperchaotic system is found as DKY= 3.1026. Since the sum of the Lyapunov exponents of the novel hyperchaotic system is negative, we deduce that the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to stabilize the novel 4-D hyperchaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 4-D hyperchaotic systems with unknown system parameters. The adaptive control results are established using Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results derived in this research work.

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

2015 ◽  
Vol 25 (3) ◽  
pp. 333-353 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Christos Volos
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Adaptive Controller ◽  
Phase Portraits ◽  
The Novel ◽  
Unknown Parameters ◽  
Mathematical Properties ◽  
Quadratic Nonlinearities

AbstractFirst, 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.

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