Electrical and Electronic Engineering - Research Publications
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ItemAnalytic synchronization conditions for a network of Wilson and Cowan oscillators(IEEE, 2015)We investigate the problem of synchronization in a network of homogeneous Wilson-Cowan oscillators with diffusive coupling. Such networks can be used to model the behavior of populations of neurons in cortical tissue, referred to as neural mass models. A new approach is proposed to address local synchronization for these types of neural mass models. By exploiting the linearized model around a limit cycle, we analyze synchronization within a network for weak, intermediate, and strong coupling. We use two-time scale averaging and the Chetaev theorem to analytically check the absence or presence of synchronization in the network with weak coupling. We also utilize the Chetaev theorem to analytically prove synchronization death in a network with strong coupling. For intermediate coupling, we use a recently proposed numerical approach to prove synchronization in the network. Simulation results confirm and illustrate our results.
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ItemCorrigendum to "On eigenvalues of Laplacian matrix for a class of directed signed graphs" (vol 523, pg 281, 2017)(Elsevier, 2017-10-01)This note corrects an error in the results of Subsection 3.1 in authors' paper “On Eigenvalues of Laplacian Matrix for a Class of Directed Signed Graphs”, which appeared in Linear Algebra and its Applications 523 (2017), 281–306.
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ItemOn eigenvalues of Laplacian matrix for a class of directed signed graphs(ELSEVIER SCIENCE INC, 2017-06-15)The eigenvalues of the Laplacian matrix for a class of directed graphs with both positive and negative weights are studied. The Laplacian matrix naturally arises in a wide range of applications involving networks. First, a class of directed signed graphs is studied in which one pair of nodes (either connected or not) is perturbed with negative weights. A necessary and sufficient condition is proposed to attain the following objective for the perturbed graph: the real parts of the non-zero eigenvalues of its Laplacian matrix are positive. Under certain assumption on the unperturbed graph, it is established that the objective is achieved if and only if the magnitudes of the added negative weights are smaller than an easily computable upper bound. This upper bound is shown to depend on the topology of the unperturbed graph. It is also pointed out that the obtained condition can be applied in a recursive manner to deal with multiple edges with negative weights. Secondly, for directed graphs, a subset of pairs of nodes are identified where if any of the pairs is connected by an edge with infinitesimal negative weight, the resulting Laplacian matrix will have at least one eigenvalue with negative real part. Illustrative examples are presented to show the applicability of our results.
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ItemOn synchronization of networks of Wilson-Cowan oscillators with diffusive coupling(PERGAMON-ELSEVIER SCIENCE LTD, 2016-09)We investigate the problem of synchronization in a network of homogeneous Wilson-Cowan oscillators with diffusive coupling. Such networks can be used to model the behavior of populations of neurons in cortical tissue, referred to as neural mass models. A new approach is proposed to address conditions for local synchronization for this type of neural mass models. By analyzing the linearized model around a limit cycle, we study synchronization within a network with direct coupling. We use both analytical and numerical approaches to link the presence or absence of synchronized behavior to the location of eigenvalues of the Laplacian matrix. For the analytical part, we apply two-time scale averaging and the Chetaev theorem, while, for the remaining part, we use a recently proposed numerical approach. Sufficient conditions are established to highlight the effect of network topology on synchronous behavior when the interconnection is undirected. These conditions are utilized to address points that have been previously reported in the literature through simulations: synchronization might persist or vanish in the presence of perturbation in the interconnection gains. Simulation results confirm and illustrate our results.
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ItemCloseness of Solutions for Singularly Perturbed Systems via Averaging(IEEE, 2018)This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary layer solutions converge to a bounded set, results on the closeness of solutions of the singularly perturbed system to the solutions of the reduced average and boundary layer systems over a finite time interval are presented. The closeness of solutions error is shown to be of order O (√{ε}), where ε is the perturbation parameter.
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ItemBifurcation analysis of two coupled Jansen-Rit neural mass models(PUBLIC LIBRARY SCIENCE, 2018-03-27)We investigate how changes in network structure can lead to pathological oscillations similar to those observed in epileptic brain. Specifically, we conduct a bifurcation analysis of a network of two Jansen-Rit neural mass models, representing two cortical regions, to investigate different aspects of its behavior with respect to changes in the input and interconnection gains. The bifurcation diagrams, along with simulated EEG time series, exhibit diverse behaviors when varying the input, coupling strength, and network structure. We show that this simple network of neural mass models can generate various oscillatory activities, including delta wave activity, which has not been previously reported through analysis of a single Jansen-Rit neural mass model. Our analysis shows that spike-wave discharges can occur in a cortical region as a result of input changes in the other region, which may have important implications for epilepsy treatment. The bifurcation analysis is related to clinical data in two case studies.