Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors
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...
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| Formato: | Online |
| Lenguaje: | inglés |
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MDPI - Multidisciplinary Digital Publishing Institute
2021
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| Acceso en línea: | 33728 |
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| _version_ | 1869520775466188800 |
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| author | Kengne, Jacques Munoz-Pacheco, Jesus M. Rajagopal, Karthikeyan Jafari, Sajad Volos, Christos |
| author_browse | Jafari, Sajad Kengne, Jacques Munoz-Pacheco, Jesus M. Rajagopal, Karthikeyan Volos, Christos |
| author_facet | Kengne, Jacques Munoz-Pacheco, Jesus M. Rajagopal, Karthikeyan Jafari, Sajad Volos, Christos |
| author_sort | Kengne, Jacques |
| collection | Directory of Open Access Books |
| description | 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. |
| format | Online |
| id | doab-20.500.12854ir-54755 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-547552024-04-11T15:10:14Z Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors Kengne, Jacques Munoz-Pacheco, Jesus M. Rajagopal, Karthikeyan Jafari, Sajad Volos, Christos TA1-2040 T1-995 S-Box algorithm empirical mode decomposition service game existence hyperchaotic system static memory complex-variable chaotic system neural network fractional-order permutation entropy adaptive approximator-based control BOPS Bogdanov Map complex systems Thurston’s algorithm parameter estimation fractional discrete chaos full state hybrid projective synchronization self-excited attractor stability PRNG inverse full state hybrid projective synchronization entropy measure chaos chaotic flow multistable core entropy multiscale multivariate entropy multistability new chaotic system strange attractors chaotic systems spatial dynamics spectral entropy resonator stochastic (strong) entropy solution multichannel supply chain Hubbard tree approximate entropy circuit design coexistence sample entropy chaotic maps chaotic map Gaussian mixture model entropy laser Non-equilibrium four-dimensional chaotic system multiple attractors projective synchronization hidden attractors hidden attractor chaotic system entropy analysis self-excited attractors multiple-valued self-reproducing system implementation unknown complex parameters optimization methods image encryption generalized synchronization uncertain dynamics fractional order nonlinear transport equation external rays Lyapunov exponents inverse generalized synchronization fixed point uniqueness electronic circuit realization synchronization Hopf bifurcation thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TB Technology: general issues::TBX History of engineering and technology 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. 2021-02-11T21:07:48Z 2021-02-11T21:07:48Z 2019-06-26 10:09:00 2019 book 33728 9783038978992 9783038978985 https://directory.doabooks.org/handle/20.500.12854/54755 eng image/jpeg Attribution-NonCommercial-NoDerivatives 4.0 International https://mdpi.com/books/pdfview/book/1279 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-03897-899-2 10.3390/books978-3-03897-899-2 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783038978992 9783038978985 290 open access |
| spellingShingle | TA1-2040 T1-995 S-Box algorithm empirical mode decomposition service game existence hyperchaotic system static memory complex-variable chaotic system neural network fractional-order permutation entropy adaptive approximator-based control BOPS Bogdanov Map complex systems Thurston’s algorithm parameter estimation fractional discrete chaos full state hybrid projective synchronization self-excited attractor stability PRNG inverse full state hybrid projective synchronization entropy measure chaos chaotic flow multistable core entropy multiscale multivariate entropy multistability new chaotic system strange attractors chaotic systems spatial dynamics spectral entropy resonator stochastic (strong) entropy solution multichannel supply chain Hubbard tree approximate entropy circuit design coexistence sample entropy chaotic maps chaotic map Gaussian mixture model entropy laser Non-equilibrium four-dimensional chaotic system multiple attractors projective synchronization hidden attractors hidden attractor chaotic system entropy analysis self-excited attractors multiple-valued self-reproducing system implementation unknown complex parameters optimization methods image encryption generalized synchronization uncertain dynamics fractional order nonlinear transport equation external rays Lyapunov exponents inverse generalized synchronization fixed point uniqueness electronic circuit realization synchronization Hopf bifurcation thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TB Technology: general issues::TBX History of engineering and technology Kengne, Jacques Munoz-Pacheco, Jesus M. Rajagopal, Karthikeyan Jafari, Sajad Volos, Christos Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors |
| title | Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors |
| title_full | Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors |
| title_fullStr | Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors |
| title_full_unstemmed | Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors |
| title_short | Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors |
| title_sort | nonlinear dynamics and entropy of complex systems with hidden and self excited attractors |
| topic | TA1-2040 T1-995 S-Box algorithm empirical mode decomposition service game existence hyperchaotic system static memory complex-variable chaotic system neural network fractional-order permutation entropy adaptive approximator-based control BOPS Bogdanov Map complex systems Thurston’s algorithm parameter estimation fractional discrete chaos full state hybrid projective synchronization self-excited attractor stability PRNG inverse full state hybrid projective synchronization entropy measure chaos chaotic flow multistable core entropy multiscale multivariate entropy multistability new chaotic system strange attractors chaotic systems spatial dynamics spectral entropy resonator stochastic (strong) entropy solution multichannel supply chain Hubbard tree approximate entropy circuit design coexistence sample entropy chaotic maps chaotic map Gaussian mixture model entropy laser Non-equilibrium four-dimensional chaotic system multiple attractors projective synchronization hidden attractors hidden attractor chaotic system entropy analysis self-excited attractors multiple-valued self-reproducing system implementation unknown complex parameters optimization methods image encryption generalized synchronization uncertain dynamics fractional order nonlinear transport equation external rays Lyapunov exponents inverse generalized synchronization fixed point uniqueness electronic circuit realization synchronization Hopf bifurcation thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TB Technology: general issues::TBX History of engineering and technology |
| topic_facet | TA1-2040 T1-995 S-Box algorithm empirical mode decomposition service game existence hyperchaotic system static memory complex-variable chaotic system neural network fractional-order permutation entropy adaptive approximator-based control BOPS Bogdanov Map complex systems Thurston’s algorithm parameter estimation fractional discrete chaos full state hybrid projective synchronization self-excited attractor stability PRNG inverse full state hybrid projective synchronization entropy measure chaos chaotic flow multistable core entropy multiscale multivariate entropy multistability new chaotic system strange attractors chaotic systems spatial dynamics spectral entropy resonator stochastic (strong) entropy solution multichannel supply chain Hubbard tree approximate entropy circuit design coexistence sample entropy chaotic maps chaotic map Gaussian mixture model entropy laser Non-equilibrium four-dimensional chaotic system multiple attractors projective synchronization hidden attractors hidden attractor chaotic system entropy analysis self-excited attractors multiple-valued self-reproducing system implementation unknown complex parameters optimization methods image encryption generalized synchronization uncertain dynamics fractional order nonlinear transport equation external rays Lyapunov exponents inverse generalized synchronization fixed point uniqueness electronic circuit realization synchronization Hopf bifurcation thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TB Technology: general issues::TBX History of engineering and technology |
| url | 33728 |
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