About the Concept of Quantum Chaos

Gomez, Ignacio S.; Losada, Marcelo; Lombardi, Olímpia

doi:10.3390/e19050205

Cited by 10 publications

(7 citation statements)

References 74 publications

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“…It is possible to find at least 35 works [ 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 , 90 , 91 ] in the Entropy journal that relate chaos theory in different areas; however, there are only five articles, from all areas, where reproducibility was mentioned [ 92 , 93 , 94 , 95 , 96 ]. From those aforementioned papers, only Funabashi [ 95 ] presented some slight relationship with the reproducibility of nonlinear dynamics fields.…”

Section: Related Workmentioning

confidence: 99%

A Note on the Reproducibility of Chaos Simulation

Nazare

Nepomuceno

Martins

et al. 2020

Entropy

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An evergreen scientific feature is the ability for scientific works to be reproduced. Since chaotic systems are so hard to understand analytically, numerical simulations assume a key role in their investigation. Such simulations have been considered as reproducible in many works. However, few studies have focused on the effects of the finite precision of computers on the simulation reproducibility of chaotic systems; moreover, code sharing and details on how to reproduce simulation results are not present in many investigations. In this work, a case study of reproducibility is presented in the simulation of a chaotic jerk circuit, using the software LTspice. We also employ the OSF platform to share the project associated with this paper. Tests performed with LTspice XVII on four different computers show the difficulties of simulation reproducibility by this software. We compare these results with experimental data using a normalised root mean square error in order to identify the computer with the highest prediction horizon. We also calculate the entropy of the signals to check differences among computer simulations and the practical experiment. The methodology developed is efficient in identifying the computer with better performance, which allows applying it to other cases in the literature. This investigation is fully described and available on the OSF platform.

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Section: Related Workmentioning

confidence: 99%

A Note on the Reproducibility of Chaos Simulation

Nazare

Nepomuceno

Martins

et al. 2020

Entropy

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“…Beyond the analysis of bifurcation diagrams and Lyapunov exponents, entropy is often studied for a broader understanding of the dynamical characteristics of systems [37]. In fact, entropy of a system is characterized by unpredictability of its dynamics, so that more complex systems are less predictable [38].…”

Section: Entropy Analysismentioning

confidence: 99%

A financial hyperchaotic system with coexisting attractors: Dynamic investigation, entropy analysis, control and synchronization

Jahanshahi

Yousefpour

Wei

et al. 2019

Chaos, Solitons & Fractals

134

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This paper is concerned with dynamic and entropy analyses of a hyperchaotic financial system, as well as with its hyperchaos suppression and synchronization. The dynamic behaviour of the system is analyzed for several parameters and initial conditions making use of bifurcation diagrams, Lyapunov exponents and phase portraits. Moreover, entropy from resulting time series is also characterized by estimating ordinal pattern distributions. These analyses have been able to determine and locate accurately chaotic and periodic attractors in the system, thus enabling successful design of its control. In general, financial systems are not always completely synchronized; therefore, some robust synchronization technique should be considered. This study proposes a novel fuzzy disturbance-observer based integral terminal sliding mode control method for the hyperchaotic financial system. The presented control technique guarantees robustness against uncertainties, external disturbances and control input saturation. Fuzzy rules are employed *Manuscript Click here to view linked References to adaptively tune the gains of the proposed control scheme. Also, the fuzzy inference engine avoids the chattering problem in the system response. Simulation results illustrate the efficient performance of the proposed control technique in presence of dynamic uncertainties, external disturbances and control input saturation.

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“…As well as the positive largest Lyapunov exponent, entropy has been widely used to characterize chaotic systems [ 53 ]. This measure focuses on estimating seemingly unpredictable time evolution of chaotic systems and consequently tries to flesh out chaos in terms of randomness [ 54 ].…”

Section: Entropy Analysismentioning

confidence: 99%

Entropy Analysis and Neural Network-Based Adaptive Control of a Non-Equilibrium Four-Dimensional Chaotic System with Hidden Attractors

Jahanshahi

Shahriari-kahkeshi

Alcaraz

et al. 2019

Entropy

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Today, four-dimensional chaotic systems are attracting considerable attention because of their special characteristics. This paper presents a non-equilibrium four-dimensional chaotic system with hidden attractors and investigates its dynamical behavior using a bifurcation diagram, as well as three well-known entropy measures, such as approximate entropy, sample entropy, and Fuzzy entropy. In order to stabilize the proposed chaotic system, an adaptive radial-basis function neural network (RBF-NN)–based control method is proposed to represent the model of the uncertain nonlinear dynamics of the system. The Lyapunov direct method-based stability analysis of the proposed approach guarantees that all of the closed-loop signals are semi-globally uniformly ultimately bounded. Also, adaptive learning laws are proposed to tune the weight coefficients of the RBF-NN. The proposed adaptive control approach requires neither the prior information about the uncertain dynamics nor the parameters value of the considered system. Results of simulation validate the performance of the proposed control method.

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About the Concept of Quantum Chaos

Cited by 10 publications

References 74 publications

A Note on the Reproducibility of Chaos Simulation

A Note on the Reproducibility of Chaos Simulation

A financial hyperchaotic system with coexisting attractors: Dynamic investigation, entropy analysis, control and synchronization

Entropy Analysis and Neural Network-Based Adaptive Control of a Non-Equilibrium Four-Dimensional Chaotic System with Hidden Attractors

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