Vaidyanathan S, Azar AT (2016) Generalized Projective Synchronization of a Novel Hyperchaotic Four-Wing System via Adaptive Control Method. Advances in Chaos Theory and Intelligent Control. Studies in Fuzziness and Soft Computing, Vol. 337, Springer-Verlag, Germany.
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In this research work, we announce a novel 4-D hyperchaotic four-wing system with three quadratic nonlinearities. First, this work describes the qualitative analysis of the novel 4-D hyperchaotic four-wing system. We show that the novel hyperchaotic four-wing system has a unique equilibrium point at the origin, which is a saddle-point. Thus, origin is an unstable equilibrium of the novel hyperchaotic system. The Lyapunov exponents of the novel hyperchaotic four-wing system are obtained as L1=2.5266L1=2.5266, L2=0.1053L2=0.1053, L3=0L3=0 and L4=−43.0194L4=−43.0194. Thus, the maximal Lyapunov exponent (MLE) of the novel hyperchaotic four-wing system is obtained as L1=2.5266L1=2.5266. Since the sum of the Lyapunov exponents of the novel hyperchaotic system is negative, it follows that the novel hyperchaotic system is dissipative. Also, the Kaplan-Yorke dimension of the novel four-wing chaotic system is obtained as DKY=3.0612DKY=3.0612. Finally, this work describes the generalized projective synchronization (GPS) of the identical novel hyperchaotic four-wing systems with unknown parasmeters. The GPS is a general type of synchronization, which generalizes known types of synchronization such as complete synchronization, anti-synchronization, hybrid synchronization, etc. The main GPS result via adaptive control method is proved using Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results for the novel 4-D hyperchaotic four-wing system.