Chimera Structures in the Ensembles of Nonlocally Coupled Chaotic Oscillators

Анищенко, В. С.; Strelkova, Galina I.

doi:10.1007/s11141-019-09926-5

Cited by 5 publications

(5 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To illustrate the impact of the proposed optimization technique on large-scale systems simulation, we considered a second test problem-a network of N coupled oscillators. Each oscillator can be described using the following equations [28]: The oscillators were coupled in the ring topology through variable x by the following coupling function [29]:…”

Section: Simulation Of Coupled Oscillators Networkmentioning

confidence: 99%

See 1 more Smart Citation

Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods

Тутуева

Butusov

2021

Mathematics

View full text Add to dashboard Cite

The increasing complexity of advanced devices and systems increases the scale of mathematical models used in computer simulations. Multiparametric analysis and study on long-term time intervals of large-scale systems are computationally expensive. Therefore, efficient numerical methods are required to reduce time costs. Recently, semi-explicit and semi-implicit Adams–Bashforth–Moulton methods have been proposed, showing great computational efficiency in low-dimensional systems simulation. In this study, we examine the numerical stability of these methods by plotting stability regions. We explicitly show that semi-explicit methods possess higher numerical stability than the conventional predictor–corrector algorithms. The second contribution of the reported research is a novel algorithm to generate an optimized finite-difference scheme of semi-explicit and semi-implicit Adams–Bashforth–Moulton methods without redundant computation of predicted values that are not used for correction. The experimental part of the study includes the numerical simulation of the three-body problem and a network of coupled oscillators with a fixed and variable integration step and finely confirms the theoretical findings.

show abstract

Section: Simulation Of Coupled Oscillators Networkmentioning

confidence: 99%

“…where a, b, c, d, e, k 1 , k 2 , and r are free parameters. We investigated an ensemble of identical systems (12) The oscillators were coupled in the ring topology through variable x by the following coupling function [29]:…”

Section: Simulation Of Coupled Oscillators Networkmentioning

confidence: 99%

Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods

Тутуева

Butusov

2021

Mathematics

View full text Add to dashboard Cite

show abstract

“…Later, this mixed state of coherence and incoherence was termed as "chimera, " coined by Strogatz and Abrams [2]. Initially identified in a system of identical Kuramoto oscillators, the chimera state has been pinpointed in a variety of other network models such as FitzHugh-Nagumo oscillators [3,4], Rössler oscillators [5], van der Pol oscillators [6], coupled Rulkov maps [7], coupled maps [8], coupled chaotic oscillators [9], multi-layer neuronal models [10], Morris-Lecar neurons [11], modular neural network [12], neuronal network model of the cat brain [13], and data-driven model of the brain [14]. Over the years, the researchers have spotted similar fascinating chimeric patterns and labeled them as virtual chimera [15], traveling chimera [16], breathing chimera [17], spike-burst chimera states [18], and others [19,20].…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Assisted Chimera and Solitary States in Networks

et al. 2021

View full text Add to dashboard Cite

Chimera and Solitary states have captivated scientists and engineers due to their peculiar dynamical states corresponding to co-existence of coherent and incoherent dynamical evolution in coupled units in various natural and artificial systems. It has been further demonstrated that such states can be engineered in systems of coupled oscillators by suitable implementation of communication delays. Here, using supervised machine learning, we predict (a) the precise value of delay which is sufficient for engineering chimera and solitary states for a given set of system's parameters, as well as (b) the intensity of incoherence for such engineered states. Ergo, using few initial data points we generate a machine learning model which can then create a more refined phase plot as well as by including new parameter values. We demonstrate our results for two different examples consisting of single layer and multi layer networks. First, the chimera states (solitary states) are engineered by establishing delays in the neighboring links of a node (the interlayer links) in a 2-D lattice (multiplex network) of oscillators. Then, different machine learning classifiers, K-nearest neighbors (KNN), support vector machine (SVM) and multi-layer perceptron neural network (MLP-NN) are employed by feeding the data obtained from the network models. Once a machine learning model is trained using the limited amount of data, it predicts the precise value of critical delay as well as the intensity of incoherence for a given unknown systems parameters values. Testing accuracy, sensitivity, and specificity analysis reveal that MLP-NN classifier is better suited than Knn or SVM classifier for the predictions of parameters values for engineered chimera and solitary states. The technique provides an easy methodology to predict critical delay values as well as intensity of incoherence for that delay value for designing an experimental setup to create solitary and chimera states.

show abstract

“…For example, some metrics, including the largest Lyapunov exponent, are reliably calculated only over a large time interval [27][28][29]. Moreover, the study of chimera states in ensembles of coupled oscillators also implies long-term simulation [30]. In both cases, the considered techniques for avoiding dynamical degradation can distort the results of the analysis.…”

Section: Introductionmentioning

confidence: 99%

Avoiding Dynamical Degradation in Computer Simulation of Chaotic Systems Using Semi-Explicit Integration: Rössler Oscillator Case

Тутуева

Butusov

2021

Fractal Fract

View full text Add to dashboard Cite

Dynamical degradation is a known problem in the computer simulation of chaotic systems. Data type limitations, sampling, and rounding errors give rise to the periodic behavior. In applications of chaotic systems in secure communication and cryptography systems, such effects can reduce data storage security and operation. In this study, we considered a possible solution to this problem by using semi-explicit integration. The key idea is to perturb the chaotic trajectory by switching between two integrators, which possess close but still different numerical solutions. Compared with the traditional approach based on the perturbation of the bifurcation parameter, this technique does not significantly change the nonlinear properties of the system. We verify the efficiency of the proposed perturbation method through several numerical experiments using the well-known Rössler oscillator.

show abstract

Chimera Structures in the Ensembles of Nonlocally Coupled Chaotic Oscillators

Cited by 5 publications

References 48 publications

Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods

Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods

Machine Learning Assisted Chimera and Solitary States in Networks

Avoiding Dynamical Degradation in Computer Simulation of Chaotic Systems Using Semi-Explicit Integration: Rössler Oscillator Case

Contact Info

Product

Resources

About