Delay engineered solitary states in complex networks

Schülen, Leonhard; Ghosh, Saptarshi; Kachhvah, Ajay Deep; Zakharova, Anna; Jalan, Sarika

doi:10.1016/j.chaos.2019.07.046

Cited by 21 publications

(9 citation statements)

References 39 publications

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“…Solitary states are described as states for which only one single element behaves differently compared with the behavior of the background group, i.e., the neighboring elements. These kinds of states have been observed in generalized Kuramoto-Sakaguchi models [MAI14a, WU18a, TEI19, CHE19b], the Kuramoto model with inertia [JAR15, JAR18], models of power grids [TAH19,HEL20], the Stuart-Landau model [SAT19], the FitzHugh-Nagumo model [RYB19a,SCH19a], systems of excitable units [ZAK16b] as well as in Lozi maps [RYB17] and even in experimental setups of coupled pendula [KAP14]. Solitary states are considered as important states in the transition from coherent to incoherent dynamics [JAR15,SEM15b,MIK18].…”

Section: Synchronization and Collective Phenomenamentioning

confidence: 99%

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Berner¹

2021

Springer Theses

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Collective phenomena in systems of interconnected dynamical units are omnipresent in nature. The swarm behavior in flocks of birds or schools of fish, the synchronous flashing of fireflies or even coherent spiking of neurons in the human brain are just a few examples of collective motion. Elucidating the mechanisms that give rise to synchronization is crucial in order to understand biological self-organization. For this sake, the theory of dynamical networks has been successfully applied over the last decades to boil down the complex dynamics from natural systems to their essentials. In addition, dynamical networks with adaptive couplings and hence non-constant network structure appear naturally in real-world systems such as power grid networks, social networks as well as neuronal networks. In this thesis, we study adaptive networks and their properties which give rise to the emergence of a variety of synchronization patterns, including complete and cluster synchronization as well as solitary and chimera-like states. One of the main fields of application that is investigated in this thesis concerns neuroscience. However, the methods and approaches developed in this work are not restricted to a specific field of application.aus gekoppelten Phasenoszillatoren an und zeigen, wie das subtile Zusammenspiel zwischen Adaptivität und Netzwerkstruktur die Entstehung komplexer partieller Synchronisationsmuster hervorruft.Trotz des regen Interesses an adaptiven Netzwerken ist über das Zusammenspiel adaptiv gekoppelter Netzwerkgruppen wenig bekannt. Solche adaptiven Mehrschicht-oder Multiplex-Netzwerke kommen in neuronalen Netzwerken ganz natürlich vor. Wir schlagen ein Konzept zur Erzeugung und Stabilisierung diverser partieller Synchronisationsmuster (Phasen-Cluster) in adaptiven Netzwerken vor. Wir zeigen, dass das "Multiplexen" verschiedene stabile Phasen-Cluster-Zustände induzieren kann, selbst wenn diese in den Einschicht-Systemen nicht stabil sind oder gar nicht existieren. Weiterhin entwickeln wir eine Methode zur Analyse von Laplace-Matrizen von Multiplex-Netzwerken, die einen Einblick in die spektrale Struktur dieser Netzwerke ermöglicht und damit eine Reduktion des Stabilitätsproblems auf die von Einschicht-Netzwerken ermöglicht. Wir setzen die neue Methode ein, um analytische Ergebnisse für die Stabilität der Zustände im Mehrschicht-System zu erhalten.

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Section: Synchronization and Collective Phenomenamentioning

confidence: 99%

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Berner¹

2021

Springer Theses

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“…Here, we consider the oscillatory regime and fix a = 0.5. Furthermore, the FHN model, considered here, includes direct as well as cross couplings between activator u i and inhibitor v i variables, which is encoded by a rotational coupling matrix [60]…”

Section: Coupled Fitzhugh-nagumo (Fhn) Oscillatorsmentioning

confidence: 99%

“…For detailed explanation on the choice of the systems parameters can be found in Ref. [60]. non-linear dynamics community to understand diverse spatio-temporal phenomena in a wide range of real world networks [63] among which chimera has also been shown in both single [7] and multiplex networks [6].…”

Section: Coupled Fitzhugh-nagumo (Fhn) Oscillatorsmentioning

confidence: 99%

Identification of Chimera using Machine Learning

Ganaie,

Ghosh,

Mendola

et al. 2020

Preprint

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Coupled dynamics on the network models have been tremendously helpful in getting insight into complex spatiotemporal dynamical patterns of a wide variety of large-scale real-world complex systems. Chimera, a state of coexistence of incoherence and coherence, is one of such patterns arising in identically coupled oscillators, which has recently drawn tremendous attention due to its peculiar nature and wide applicability, specially in neuroscience. The identification of chimera is a challenging problem due to ambiguity in its appearance. We present a distinctive approach to identify and characterize the chimera state using machine learning techniques, namely random forest, oblique random forests via multi-surface proximal support vector machines (MPRaF-T, P, N) and sparse pre-trained / auto-encoder based random vector functional link neural network (RVFL-AE). We demonstrate high accuracy in identifying the coherent, incoherent and chimera states from given spatial profiles. We validate this approach for different time-continuous and time discrete coupled dynamics on networks. This work provides a direction for employing machine learning techniques to identify dynamical patterns arising due to the interaction among non-linear units on large-scale, and for characterizing complex spatio-temporal phenomena in real-world systems for various applications.The identification and characterization of chimera state in various complex dynamical systems is a challenging but essential task, given its new-found applicability in various areas. Recently, machine learning (ML) techniques have demonstrated tremendous promise in various areas of nonlinear dynamics and network science. Here, we present a universal machine learning-based approach towards the identification of chimera states by utilizing five ML algorithms, namely RaF, MPRaF-T, P, N, and RVFL-AE, trained on mere dynamical spatial configurations as input. This technique can characterize different dynamical states and identify chimera patterns in various time-discrete and time-continuous model systems.

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“…Hence, k-solitary states comprise k isolated elements [25]. Recently, the existence of solitary states has been demonstrated in a network of ensembles having attractive and repulsive interactions at the edge of synchrony [26] and partial synchrony [27], inertial Kuramoto model [28], oscillators with negative time-delayed feedback under external forcing [29], identical populations of Stuart-Landau oscillators [30], FitzHugh-Nagumo neurons in the oscillatory regime [4], and neuronal oscillators and coupled chaotic maps in the presence of delayed links [31]. The occurrence of solitary states can be observed in power grid networks in which individual gridunits gradually desynchronize during a partial or complete blackout [32].…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Assisted Chimera and Solitary States in Networks

et al. 2021

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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.

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Delay engineered solitary states in complex networks

Cited by 21 publications

References 39 publications

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Identification of Chimera using Machine Learning

Machine Learning Assisted Chimera and Solitary States in Networks

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