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Entropy in Dynamic Systems
Jan Awrejcewicz and J. A. Tenreiro Machado
2019
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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.
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Keywords
- (asymptotical) focal entropy point
- Adomian decomposition
- analytical solution
- approximate entropy
- Benettin method
- Bernoulli–Euler beam
- bounded chaos
- Chua’s system
- colored noise
- conditional Tsallis entropy
- continuous flow
- descriptor fractional linear systems
- deterministic chaos
- discrete chaos
- discrete fractional calculus
- discrete mapping
- disturbation
- dynamical system
- Fourier spectrum
- fractional Brownian motion
- Fractional calculus
- fractional stochastic partial differential equation
- Gauss wavelets
- Gaussian white noise
- geometric nonlinearity
- hidden attractors
- hyperchaotic system
- image encryption
- information transfer
- Kantz method
- Lorenz system
- Lyapunov exponents
- m-dimensional manifold
- method of synchronization
- Mittag–Leffler function
- multi-time scale fractional stochastic differential equations
- n/a
- neural network method
- noise induced transitions
- nonautonomous (autonomous) dynamical system
- partition
- permutation entropy
- phase-locked loop
- product MV-algebra
- random number generator
- regular pencils
- Rosenstein method
- Schur factorization
- self-synchronous stream cipher
- stabilization
- topological entropy
- true chaos
- Tsallis entropy
- unbounded chaos
- wavelet transform
- wavelets
- Wolf method
Links
DOI: 10.3390/books978-3-03921-617-8Editions
