Entropy in Dynamic Systems

• Main Author: Awrejcewicz, Jan (auth)
• Other Authors: Tenreiro Machado, J. A. (auth)
• Format: Electronic Book Chapter
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2019
• Subjects: History of engineering & technology; n/a; nonautonomous (autonomous) dynamical system; stabilization; multi-time scale fractional stochastic differential equations; conditional Tsallis entropy; wavelet transform; hyperchaotic system; Chua's system; permutation entropy; neural network method; Information transfer; self-synchronous stream cipher; colored noise; Benettin method; method of synchronization; topological entropy; geometric nonlinearity; Kantz method; dynamical system; Gaussian white noise; phase-locked loop; wavelets; Rosenstein method; m-dimensional manifold; deterministic chaos; disturbation; Mittag-Leffler function; approximate entropy; bounded chaos; Adomian decomposition; fractional calculus; product MV-algebra; Tsallis entropy; descriptor fractional linear systems; analytical solution; fractional Brownian motion; true chaos; discrete mapping; partition; unbounded chaos; fractional stochastic partial differential equation; noise induced transitions; random number generator; Fourier spectrum; hidden attractors; (asymptotical) focal entropy point; regular pencils; continuous flow; Bernoulli-Euler beam; image encryption; Gauss wavelets; Lyapunov exponents; discrete fractional calculus; Lorenz system; Schur factorization; discrete chaos; Wolf method
• Online Access: DOAB: download the publication; DOAB: description of the publication

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.