Entropy in Dynamic Systems
Awrejcewicz, Jan
Entropy in Dynamic Systems - MDPI - Multidisciplinary Digital Publishing Institute 2019 - 1 electronic resource (172 p.)
Open Access
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.
Creative Commons
English
books978-3-03921-617-8 9783039216161 9783039216178
10.3390/books978-3-03921-617-8 doi
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
Entropy in Dynamic Systems - MDPI - Multidisciplinary Digital Publishing Institute 2019 - 1 electronic resource (172 p.)
Open Access
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.
Creative Commons
English
books978-3-03921-617-8 9783039216161 9783039216178
10.3390/books978-3-03921-617-8 doi
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