9 research outputs found
Machine Learning assisted Chimera and Solitary states in Networks
Chimera and Solitary states have captivated scientists and engineers due to
their peculiar dynamical states corresponding to the 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 the 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 parameters, as well as (b) the
intensity of incoherence for such engineered states. The results are
demonstrated 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, KNN, SVM and MLP-Neural Network are employed by feeding
the data obtained from the network models. Once a machine learning model is
trained using a limited amount of data, it makes predictions for a given
unknown systems parameter 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 the intensity of incoherence for designing an
experimental setup to create solitary and chimera states.Comment: 11 Pages, 9 Figures, Contains revised abstract and publication
detail
Complex partial synchronization patterns in networks of delay-coupled neurons
We study the spatio-temporal dynamics of a multiplex network of delay-coupled FitzHugh–Nagumo oscillators with non-local and fractal connectivities. Apart from chimera states, a new regime of coexistence of slow and fast oscillations is found. An analytical explanation for the emergence of such coexisting partial synchronization patterns is given. Furthermore, we propose a control scheme for the number of fast and slow neurons in each layer.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept
Chimeras in Multiplex Networks: Interplay of Inter- and Intra-Layer Delays
Time delay in complex networks with multiple interacting layers gives rise to special dynamics. We study the scenarios of time delay induced patterns in a three-layer network of FitzHugh-Nagumo oscillators. The topology of each layer is given by a nonlocally coupled ring. For appropriate values of the time delay in the couplings between the nodes, we find chimera states, i.e., hybrid spatio-temporal patterns characterized by coexisting domains with incoherent and coherent dynamics. In particular, we focus on the interplay of time delay in the intra-layer and inter-layer coupling term. In the parameter plane of the two delay times we find regions where chimera states are observed alternating with coherent dynamics. Moreover, in the presence of time delay we detect full and relay inter-layer synchronization.DFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität BerlinDFG, SFB 910, Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept
Composed solutions of synchronized patterns in multiplex networks of Kuramoto oscillators
Networks with different levels of interactions, including multilayer and
multiplex networks, can display a rich diversity of dynamical behaviors and can
be used to model and study a wide range of systems. Despite numerous efforts to
investigate these networks, obtaining mathematical descriptions for the
dynamics of multilayer and multiplex systems is still an open problem. Here, we
combine ideas and concepts from linear algebra and graph theory with nonlinear
dynamics to offer a novel approach to study multiplex networks of Kuramoto
oscillators. Our approach allows us to study the dynamics of a large, multiplex
network by decomposing it into two smaller systems: one representing the
connection scheme within layers (intra-layer), and the other representing the
connections between layers (inter-layer). Particularly, we use this approach to
compose solutions for multiplex networks of Kuramoto oscillators. These
solutions are given by a combination of solutions for the smaller systems given
by the intra and inter-layer system and, in addition, our approach allows us to
study the linear stability of these solutions
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Synchronization Patterns in Modular Neuronal Networks: A Case Study of C. elegans
We investigate synchronization patterns and chimera-like states in the modular multilayer topology of the connectome of Caenorhabditis elegans. In the special case of a designed network with two layers, one with electrical intra-community links and one with chemical inter-community links, chimera-like states are known to exist. Aiming at a more biological approach based on the actual connectivity data, we consider a network consisting of two synaptic (electrical and chemical) and one extrasynaptic (wireless) layers. Analyzing the structure and properties of this layered network using Multilayer-Louvain community detection, we identify modules whose nodes are more strongly coupled with each other than with the rest of the network. Based on this topology, we study the dynamics of coupled Hindmarsh-Rose neurons. Emerging synchronization patterns are quantified using the pairwise Euclidean distances between the values of all oscillators, locally within each community and globally across the network. We find a tendency of the wireless coupling to moderate the average coherence of the system: for stronger wireless coupling, the levels of synchronization decrease both locally and globally, and chimera-like states are not favored. By introducing an alternative method to define meaningful communities based on the dynamical correlations of the nodes, we obtain a structure that is dominated by two large communities. This promotes the emergence of chimera-like states and allows to relate the dynamics of the corresponding neurons to biological neuronal functions such as motor activities. © Copyright © 2019 Pournaki, Merfort, Ruiz, Kouvaris, Hövel and Hizanidis
Optimal self-induced stochastic resonance in multiplex neural networks: electrical versus chemical synapses
Electrical and chemical synapses shape the dynamics of neural networks and
their functional roles in information processing have been a longstanding
question in neurobiology. In this paper, we investigate the role of synapses on
the optimization of the phenomenon of self-induced stochastic resonance in a
delayed multiplex neural network by using analytical and numerical methods. We
consider a two-layer multiplex network, in which at the intra-layer level
neurons are coupled either by electrical synapses or by inhibitory chemical
synapses. For each isolated layer, computations indicate that weaker electrical
and chemical synaptic couplings are better optimizers of self-induced
stochastic resonance. In addition, regardless of the synaptic strengths,
shorter electrical synaptic delays are found to be better optimizers of the
phenomenon than shorter chemical synaptic delays, while longer chemical
synaptic delays are better optimizers than longer electrical synaptic delays --
in both cases, the poorer optimizers are in fact worst. It is found that
electrical, inhibitory, or excitatory chemical multiplexing of the two layers
having only electrical synapses at the intra-layer levels can each optimize the
phenomenon. And only excitatory chemical multiplexing of the two layers having
only inhibitory chemical synapses at the intra-layer levels can optimize the
phenomenon. These results may guide experiments aimed at establishing or
confirming the mechanism of self-induced stochastic resonance in networks of
artificial neural circuits, as well as in real biological neural networks.Comment: 24 pages, 7 figure