Machine Learning Assisted Chimera and Solitary States in Networks

Niraj Kushwaha,Naveen Kumar Mendola,Ajay Deep Kachhvah,Sarika Jalan,Saptarshi Ghosh

doi:10.3389/fphy.2021.513969

Niraj Kushwaha, Naveen Kumar Mendola + Show 3 more

Open Access

https://doi.org/10.3389/fphy.2021.513969

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Abstract

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.

Highlights

In the year 2002, a new area was introduced in the field of nonlinear dynamics when Kuramoto et al brought to light the phenomenon of occurrence of symmetry breaking in a system of identically coupled oscillators [1]
Thereafter, we make predictions for the precise value of critical delay required for the engineering chimera states and solitary states by employing machine learning classifiers
When a delay is instituted in all the neighboring links to a node of the lattice, this produces the perturbation in the neighboring links and giving rise to chimera states

Summary

Introduction

In the year 2002, a new area was introduced in the field of nonlinear dynamics when Kuramoto et al brought to light the phenomenon of occurrence of symmetry breaking in a system of identically coupled oscillators [1]. Apart from synchronous and asynchronous states, they identified a remarkable hybrid dynamical structure where both the asynchronous and synchronous regions coexisted in a system of identical oscillators. Later, this mixed state of coherence and incoherence was termed as “chimera,” coined by Strogatz and Abrams [2]. A comprehensive review on the development of chimera states in a variety of systems can be found in [23, 24]

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