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Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors
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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.
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Keywords
- adaptive approximator-based control
- approximate entropy
- Bogdanov Map
- BOPS
- Chaos
- chaotic flow
- chaotic map
- chaotic maps
- chaotic system
- chaotic systems
- circuit design
- Coexistence
- complex systems
- complex-variable chaotic system
- core entropy
- electronic circuit realization
- empirical mode decomposition
- Entropy
- entropy analysis
- entropy measure
- existence
- external rays
- fixed point
- fractional discrete chaos
- fractional order
- fractional-order
- full state hybrid projective synchronization
- Gaussian mixture model
- generalized synchronization
- hidden attractor
- hidden attractors
- Hopf bifurcation
- Hubbard tree
- hyperchaotic system
- image encryption
- implementation
- inverse full state hybrid projective synchronization
- inverse generalized synchronization
- laser
- Lyapunov exponents
- multichannel supply chain
- multiple attractors
- multiple-valued
- multiscale multivariate entropy
- multistability
- multistable
- Neural Network
- new chaotic system
- Non-equilibrium four-dimensional chaotic system
- nonlinear transport equation
- optimization methods
- Parameter estimation
- permutation entropy
- PRNG
- projective synchronization
- resonator
- S-Box algorithm
- sample entropy
- self-excited attractor
- self-excited attractors
- self-reproducing system
- service game
- spatial dynamics
- spectral entropy
- Stability
- static memory
- stochastic (strong) entropy solution
- strange attractors
- Synchronization
- Thurston’s algorithm
- uncertain dynamics
- Uniqueness
- unknown complex parameters
Links
DOI: 10.3390/books978-3-03897-899-2Editions
