Chaotic systems
View article: Spectral Statistics in Spatially Extended Chaotic Quantum Many-Body Systems
Spectral Statistics in Spatially Extended Chaotic Quantum Many-Body Systems Open
We study spectral statistics in spatially extended chaotic quantum many-body systems, using simple lattice Floquet models without time-reversal symmetry. Computing the spectral form factor K(t) analytically and numerically, we show that it…
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Large-Scale Optical Reservoir Computing for Spatiotemporal Chaotic Systems Prediction Open
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Long-term prediction of chaotic systems with machine learning Open
Reservoir computing systems, a class of recurrent neural networks, have recently been exploited for model-free, data-based prediction of the state evolution of a variety of chaotic dynamical systems. The prediction horizon demonstrated has…
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Numerical Solutions and Synchronization of a Variable-Order Fractional Chaotic System Open
In the present paper, we implement a novel numerical method for solving differential equations with fractional variable-order in the Caputo sense to research the dynamics of a circulant Halvorsen system. Control laws are derived analytical…
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Optical Reservoir Computing Using Multiple Light Scattering for Chaotic Systems Prediction Open
Reservoir Computing is a relatively recent computational framework based on a\nlarge Recurrent Neural Network with fixed weights. Many physical\nimplementations of Reservoir Computing have been proposed to improve speed and\nenergy efficie…
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Chaos synchronization in generalized Lorenz systems and an application to image encryption Open
Examples of synchronization, pervasive throughout the natural world, are often awe-inspiring because they tend to transcend our intuition. Synchronization in chaotic dynamical systems, of which the Lorenz system is a quintessential example…
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A New Chaotic S-Box Generation Method Using Parameter Optimization of One Dimensional Chaotic Maps Open
Chaotic systems have been used to generate the substitutional box structures. The existence of endless possibilities for the selection of the initial conditions and control parameters of the chaotic system has made it a necessity to use th…
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A Novel Chaotic System without Equilibrium: Dynamics, Synchronization, and Circuit Realization Open
A few special chaotic systems without unstable equilibrium points have been investigated recently. It is worth noting that these special systems are different from normal chaotic ones because the classical Shilnikov criterion cannot be use…
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Smallest chimera states Open
We demonstrate that chimera behavior can be observed in small networks consisting of three identical oscillators, with mutual all-to-all coupling. Three different types of chimeras, characterized by the coexistence of two coherent oscillat…
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Using reservoir computers to distinguish chaotic signals Open
Several recent papers have shown that reservoir computers are useful for\nanalyzing and predicting dynamical systems. Reservoir computers have also been\nshown to be useful for various classification problems. In this work, a\nreservoir co…
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Stabilization of Chaotic Systems With Both Uncertainty and Disturbance by the UDE-Based Control Method Open
This paper investigates the stabilization of a class of chaotic systems with both model uncertainty and external disturbance. By combining the dynamic feedback control method, and the uncertainty and disturbance estimator (UDE)-based contr…
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Robust Synchronization of Fractional-Order Uncertain Chaotic Systems Based on Output Feedback Sliding Mode Control Open
This paper mainly focuses on the robust synchronization issue for drive-response fractional-order chaotic systems (FOCS) when they have unknown parameters and external disturbances. In order to achieve the goal, the sliding mode control sc…
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Finite-Size Scaling of Out-of-Time-Ordered Correlators at Late Times Open
Chaotic dynamics in quantum many-body systems scrambles local information so that at late times it can no longer be accessed locally. This is reflected quantitatively in the out-of-time-ordered correlator of local operators, which is expec…
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Birth and death of chimera: Interplay of delay and multiplexing Open
The chimera state with co-existing coherent-incoherent dynamics has recently\nattracted a lot of attention due to its wide applicability. We investigate\nnon-locally coupled identical chaotic maps with delayed interactions in the\nmultiple…
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Semiclassical theory of out-of-time-order correlators for low-dimensional classically chaotic systems Open
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Random Matrix Theory Approach to Chaotic Coherent Perfect Absorbers Open
We employ random matrix theory in order to investigate coherent perfect absorption (CPA) in lossy systems with complex internal dynamics. The loss strength γ_{CPA} and energy E_{CPA}, for which a CPA occurs, are expressed in terms of the e…
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Finite-time generalized synchronization of nonidentical delayed chaotic systems Open
This paper deals with the finite-time generalized synchronization (GS) problem of drive-response systems. The main purpose of this paper is to design suitable controllers to force the drive-response system realize GS in a finite time. Base…
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A Chaotic System with Infinite Equilibria and Its S-Box Constructing Application Open
Systems with many equilibrium points have attracted considerable interest recently. A chaotic system with a line equilibrium has been studied in this work. The system has infinite equilibria and exhibits coexisting chaotic attractors. The …
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Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems Open
In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditio…
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Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems Open
Designing a chaotic system with infinitely many attractors is a hot topic. In this paper, multiscale multivariate permutation entropy (MMPE) and multiscale multivariate Lempel–Ziv complexity (MMLZC) are employed to analyze the complexity o…
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On new chaotic and hyperchaotic systems: A literature survey Open
This paper provides a thorough survey of new chaotic and hyperchaotic systems. An analysis of the dynamic behavior of these complex systems is presented by pointing out their originality and elementary characteristics. Recently, such syste…
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Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points Open
Chaotic dynamics exists in many natural systems, such as weather and climate, and there are many applications in different disciplines. However, there are few research results about chaotic conservative systems especially the smooth hyperc…
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On Chaos in the Fractional-Order Discrete-Time Unified System and Its Control Synchronization Open
In this paper, we propose a fractional map based on the integer-order unified map. The chaotic behavior of the proposed map is analyzed by means of bifurcations plots, and experimental bounds are placed on the parameters and fractional ord…
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A Novel Image Encryption Scheme Using the Composite Discrete Chaotic System Open
The composite discrete chaotic system (CDCS) is a complex chaotic system that combines two or more discrete chaotic systems. This system holds the chaotic characteristics of different chaotic systems in a random way and has more complex ch…
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A 4-D chaotic hyperjerk system with a hidden attractor, adaptive backstepping control and circuit design Open
A novel 4-D chaotic hyperjerk system with four quadratic nonlinearities is presented in this work. It is interesting that the hyperjerk system has no equilibrium. A chaotic attractor is said to be a hidden attractor when its basin of attra…
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A New Pseudorandom Bit Generator Based on Mixing Three‐Dimensional Chen Chaotic System with a Chaotic Tactics Open
In this paper, a new chaotic system is proposed based on mixing three‐dimensional Chen chaotic system with a chaotic tactics. This new system is proved to be chaotic under Wiggins’ chaos definition and can generate chaotic sequences with h…
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Medical Images Encryption Based on Adaptive-Robust Multi-Mode Synchronization of Chen Hyper-Chaotic Systems Open
In this paper, a novel medical image encryption method based on multi-mode synchronization of hyper-chaotic systems is presented. The synchronization of hyper-chaotic systems is of great significance in secure communication tasks such as e…
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Spectral Lyapunov exponents in chaotic and localized many-body quantum systems Open
We consider the spectral statistics of the Floquet operator for disordered, periodically driven spin chains in their quantum chaotic and many-body localized (MBL) phases. The spectral statistics are characterized by the traces of powers t …
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Coexistence of synchronization and anti-synchronization in chaotic systems Open
The coexistence of anti-synchronization and synchronization in chaotic systems is investigated. A novel algorithm is proposed to determine the variables of the master system that should anti-synchronize with corresponding variables of the …
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A Novel Random Number Generator Based on Fractional Order Chaotic Chua System Open
One of the practical applications of chaotic systems is the design of a random number generator. In the literature, generally random number generators are designed using discrete time chaotic systems. The reason for the use of the discrete…