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Entropy in Dynamic Systems

Authors: ---
ISBN: 9783039216161 9783039216178 Year: Pages: 172 DOI: 10.3390/books978-3-03921-617-8 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:16
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Abstract

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.

Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors

Authors: --- --- --- --- et al.
ISBN: 9783038978985 9783038978992 Year: Pages: 290 DOI: 10.3390/books978-3-03897-899-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-06-26 10:09:00
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In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.

Keywords

new chaotic system --- multiple attractors --- electronic circuit realization --- S-Box algorithm --- chaotic systems --- circuit design --- parameter estimation --- optimization methods --- Gaussian mixture model --- chaotic system --- empirical mode decomposition --- permutation entropy --- image encryption --- hidden attractors --- fixed point --- stability --- nonlinear transport equation --- stochastic (strong) entropy solution --- uniqueness --- existence --- multiscale multivariate entropy --- multistability --- self-reproducing system --- chaos --- hidden attractor --- self-excited attractor --- fractional order --- spectral entropy --- coexistence --- multistability --- chaotic flow --- hidden attractor --- multistable --- entropy --- core entropy --- Thurston’s algorithm --- Hubbard tree --- external rays --- chaos --- Lyapunov exponents --- multiple-valued --- static memory --- strange attractors --- fractional discrete chaos --- entropy --- projective synchronization --- full state hybrid projective synchronization --- generalized synchronization --- inverse full state hybrid projective synchronization --- inverse generalized synchronization --- multichannel supply chain --- service game --- chaos --- entropy --- BOPS --- Hopf bifurcation --- self-excited attractors --- multistability --- sample entropy --- PRNG --- Non-equilibrium four-dimensional chaotic system --- entropy measure --- adaptive approximator-based control --- neural network --- uncertain dynamics --- synchronization --- fractional-order --- complex-variable chaotic system --- unknown complex parameters --- chaotic map --- fixed point --- chaos --- approximate entropy --- implementation --- hidden attractor --- hyperchaotic system --- multistability --- entropy analysis --- hidden attractor --- complex systems --- fractional-order --- entropy --- chaotic maps --- chaos --- spatial dynamics --- Bogdanov Map --- chaos --- laser --- resonator

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2019 (2)