Hybrid projective synchronization and control of the Baier-Sahle hyperchaotic flow in arbitrary dimensions with unknown parameters

The problem of hybrid projective synchronization (HPS) strategies and control for the Baier-Sahle hyperchaotic flow in arbitrary dimensions with unknown parameters is considered. Based on the Lasalle invariance principle and adaptive control method, adaptive controllers and parameters update laws are given for the HPS between two identical hyper-chaotic systems with fully unknown parameters. Using this method, the Baier-Sahle hyperchaotic flow in arbitrary dimensions is controlled to the unsteady equilibrium points. The Baier-Sahle hyperchaotic flow is a useful choice for this analysis, since it is a standard model of hyperchaos, yet it is simple enough to be analytically tractable. In particular, the Baier-Sahle hyperchaotic flow has been proposed as an N dimensional nonlinear system model giving the maximal number of positive Lyapunov exponents (N = 2). Both a rigorous theoretical analysis and direct numerical simulations are provided to demonstrate the control of hyperchaos in this model. The results suggest that the methods used here can be applied to more complicated models from which hyperchaos arises. (C) 2014 Elsevier Inc. All rights reserved

Hybrid Projective Synchronization And Control Of The Baier-Sahle Hyperchaotic Flow In Arbitrary Dimensions With Unknown Parameters

The problem of hybrid projective synchronization (HPS) strategies and control for the Baier-Sahle hyperchaotic flow in arbitrary dimensions with unknown parameters is considered. Based on the Lasalle invariance principle and adaptive control method, adaptive controllers and parameters update laws are given for the HPS between two identical hyper-chaotic systems with fully unknown parameters. Using this method, the Baier-Sahle hyperchaotic flow in arbitrary dimensions is controlled to the unsteady equilibrium points. The Baier-Sahle hyperchaotic flow is a useful choice for this analysis, since it is a standard model of hyperchaos, yet it is simple enough to be analytically tractable. In particular, the Baier-Sahle hyperchaotic flow has been proposed as an N dimensional nonlinear system model giving the maximal number of positive Lyapunov exponents (N-2). Both a rigorous theoretical analysis and direct numerical simulations are provided to demonstrate the control of hyperchaos in this model. The results suggest that the methods used here can be applied to more complicated models from which hyperchaos arises

Entropy in Dynamic Systems

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed