Chaos on hyperspaces García Guirao, Juan Luis; Kwietniak, Dominik; Lampart, Marek ...
Nonlinear analysis,
07/2009, Letnik:
71, Številka:
1
Journal Article
Recenzirano
Let
f
be a continuous self-map of a compact metric space
X
. The transformation
f
induces in a natural way a self-map
f
¯
defined on the hyperspace
K
(
X
)
of all nonempty closed subsets of
X
. We ...study which of the most usual notions of chaos for dynamical systems induced by
f
are inherited by
f
¯
and vice versa. We consider distributional chaos, Li–Yorke chaos,
ω
-chaos, Devaney chaos, topological chaos (positive topological entropy), specification property and their variants. This answers questions stated independently by Roman-Flores and Banks.
Based on fuzzy mathematics theory, this paper proposes a fuzzy multi-objective optimization model with related constraints to minimize the total economic cost and network loss of microgrid. ...Uncontrollable microsources are considered as negative load, and stochastic net load scenarios are generated for taking the uncertainty of their output power and load into account. Cooperating with storage devices of the optimal capacity controllable microsources are treated as variables in the optimization process with the consideration of their start and stop strategy. Chaos optimization algorithm is introduced into binary particle swarm optimization (BPSO) to propose chaotic BPSO (CBPSO). Search capability of BPSO is improved via the chaotic search approach of chaos optimization algorithm. Tests of four benchmark functions show that the proposed CBPSO has better convergence performance than BPSO. Simulation results validate the correctness of the proposed model and the effectiveness of CBPSO.
Neuromorphic Dynamics of Chua Corsage Memristor Jin, Peipei; Wang, Guangyi; Liang, Yan ...
IEEE transactions on circuits and systems. I, Regular papers,
11/2021, Letnik:
68, Številka:
11
Journal Article
Recenzirano
Odprti dostop
Neuromorphic computing can solve computationally hard problems with energy efficiencies unattainable for von Neumann architectures. A locally-active memristor, which possesses the capability to ...amplify infinitesimal fluctuations in energy and can be used to generate neuromorphic behaviors, is a natural candidate for constructing an electronic equivalent of biological neurons. This paper identifies some unknown neuromorphic dynamics of the Chua corsage memristor (CCM), and shows that the CCM, when biased at the edge of chaos domain, can exhibit rich dynamics of biological neurons. Using Chua's theories of local activity and edge of chaos, we demonstrate that under the destabilizing of the input voltage and the circuit parameters (inductance or capacitance), two CCM-based circuits can produce thirteen types of neuromorphic behaviors either on, or near the edge of chaos domain via supercritical or subcritical Hopf bifurcation. In addition, we give the conditions to test the edge of chaos of the CCM and the CCM-based circuit only by using the poles and the zero of their admittance functions.
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.
Quantifying the uncertainty of the renewable energy generation units and loads is critical to ensure the dynamic security of next-generation power systems. To achieve that goal, the time-consuming ...Monte Carlo simulations are usually used, which is not suitable for online dynamic analysis of large-scale power systems. To circumvent this difficulty, two uncertainty quantification approaches using polynomial-chaos-based methods are proposed and investigated. The first approach is the generalized polynomial chaos method that is able to reduce the computing time by three orders of magnitude compared with Monte Carlo methods while achieving the same accuracy. We find that this approach is very useful for short-term power system dynamic simulations, but it may produce unreliable results for long-term simulations. To address the weakness of that approach, we present the second method, namely the multi-element generalized-polynomial-chaos method. It is seen that this method is more accurate and more numerically stable than the generalized polynomial chaos method. Since the uncertainties of the renewable energy generation units and loads can follow very different distributions, we extend the Stieltjes' recursive procedure that allows us to derive the orthogonal basis functions for any assumed probability distribution of the input random variables. Extensive simulations carried out on the WECC 3-machine 9-bus system and the New England 10-machine 39-bus system reveal that our proposed approaches are able to produce comparable accuracy as the Monte Carlo based method while achieving significantly improved computational efficiency for both stable and unstable power system operating conditions.
•Strongly Ruelle–Takens chaos, strongly Auslander–Yorke chaos and Poincare chaos are studied on the product of semiflows.•It is proved that if the finite or the countably infinite product of ...semiflows is strongly Ruelle–Takens chaotic (resp., strongly Auslander–Yorke chaotic and Poincare chaotic) then at least one of the factors is so.•Examples/counterexamples are also provided related to our results.
In this paper, we study strongly Ruelle–Takens chaos, strongly Auslander–Yorke chaos and Poincaré chaos on the product of semiflows. It is proved that if the finite product or the countably infinite product of semiflows is chaotic then at least one of the factors is chaotic. We also provide necessary examples/counterexamples, wherever possible, related to our results.
•The nonlinear coefficient θ and the delay factor t are introduced.•The nonlinear delayed feedback logistic chaotic map (NDFL) is proposed.•The linear-nonlinear diffusion method is ...proposed.•Encryption method that mixes pixel values, pixel bits and binary bits is proposed.•The strategy of simultaneous scrambling and diffusion is adopted.
This paper proposes a new chaotic system, combined with the dynamic mixing of pixel values, pixel bits, and binary bits encryption algorithms, which are used together in image encryption. The whole process is as follows. First, the original plain text image is converted into an initial key through the SHA-512 algorithm and related operations, then the initial key is applied to the proposed delayed feedback dynamic mixed linear-nonlinear coupled mapping lattices (DFDMLNCML) to obtain the chaotic matrix required for encryption, next, perform the encryption operation of mixed pixel values, pixel bits and binary bits, scrambling and diffusion are done together to improve the security of the algorithm. Finally, the average NPCR, average UACI is 99.6075, 33.4795, respectively, experimental results and various security analyses show that the performance of the system and algorithm is good, and it can resist ordinary attacks, such as selecting plaintext attacks, cropping attacks, and noise attacks.
This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of ...van der Pol, Duffing, Ueda, Lorenz, Rössler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos. The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos.
Kicked rotor is a paradigmatic model for classical and quantum chaos in time-dependent Hamiltonian systems. More than fifty years since the introduction of this model, there is an increase in the ...number of works that use kicked rotor model as a fundamental template to study a variety of questions in nonlinear dynamics, quantum chaos, condensed matter physics and quantum information. This is aided by the experimental approaches that have implemented many variants of the quantum kicked rotor model. The problems addressed using kicked rotor and its variants include the basic phenomenology of classical and quantum chaos, transport and localization in one- and higher dimensional kicked systems, effects of disorder and interactions, resonant dynamics and the relation between quantum correlations and chaos. This would also include a range of applications such as for constructing ratchet dynamics and for atom-optics based interferometry. This article reviews the current status of theoretical and experimental research devoted to exploring these ideas using the framework of kicked rotor model.
In the search of theoretical models describing cancer, one of promising directions is chaos. It is connected to ideas of “genome chaos” and “life on the edge of chaos”, but they profoundly differ in ...the meaning of the term “chaos”. To build any coherent models, notions used by both ideas should be firstly brought closer. The hypothesis “life on the edge of chaos” using deterministic chaos has been radically deepened developed in recent years by the discovery of half-chaos. This new view requires a deeper interpretation within the range of the cell and the organism. It has impacts on understanding “chaos” in the term “genome chaos”. This study intends to present such an interpretation on the basis of which such searches will be easier and closer to intuition. We interpret genome chaos as deterministic chaos in a large module of half-chaotic network modeling the cell. We observed such chaotic modules in simulations of evolution controlled by weaker variant of natural selection. We also discuss differences between free and somatic cells in modeling their disturbance using half-chaotic networks.
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