Showing papers by "Sarika Jalan published in 2006"
TL;DR: It turns out that the global qualitative properties of the coupled dynamics can be classified into three different phases based on the synchronization of the variables and the homogeneity of the symbolic dynamics, of particular interest is the homogeneous unsynchronized phase.
Abstract: We study coupled dynamics on networks using symbolic dynamics. The symbolic dynamics is defined by dividing the state space into a small number of regions (typically 2), and considering the relative frequencies of the transitions between those regions. It turns out that the global qualitative properties of the coupled dynamics can be classified into three different phases based on the synchronization of the variables and the homogeneity of the symbolic dynamics. Of particular interest is the homogeneous unsynchronized phase, where the coupled dynamics is in a chaotic unsynchronized state, but exhibits qualitative similar symbolic dynamics at all the nodes in the network. We refer to this dynamical behavior as symbolic synchronization. In this phase, the local symbolic dynamics of any arbitrarily selected node reflects global properties of the coupled dynamics, such as qualitative behavior of the largest Lyapunov exponent and phase synchronization. This phase depends mainly on the network architecture, and only to a smaller extent on the local chaotic dynamical function. We present results for two model dynamics, iterations of the one-dimensional logistic map and the two-dimensional Henon map, as local dynamical function.
21 citations
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TL;DR: A method based on symbolic dynamics for the detection of synchronization in networks of coupled maps and distinguishing between chaotic and random iterations that is robust against parameter uncertainties, independent of the network size, and does not require knowledge of the connection structure is presented.
Abstract: We present a method based on symbolic dynamics for the detection of synchronization in networks of coupled maps and distinguishing between chaotic and random iterations. The symbolic dynamics are defined using special partitions of the phase space which prevent the occurrence of certain symbol sequences related to the characteristics of the dynamics. Synchrony in a large network can be detected using measurements from only a single node by checking for the presence of forbidden symbol transitions. The method utilises a relatively short time series of measurements and hence is computationally very fast. Furthermore, it is robust against parameter uncertainties, is independent of the network size, and does not require knowledge of the connection structure.
2 citations
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14 Aug 2006
TL;DR: The analogy between the onset of small-world behavior and the transition from Poisson to GOE statistics is shown and the eigenvalue fluctuations are shown to follow Gaussian orthogonal ensemble (GOE) statistics.
Abstract: Following random matrix theory, we study nearest neighbor spacing distribution (NNSD) of the eigenvalues of the adjacency matrix of various model networks, namely scale-free, small-world and random networks. Our analysis shows that, though spectral densities of these model networks are different, their eigenvalue fluctuations are same and follow Gaussian orthogonal ensemble (GOE) statistics. Secondly we show the analogy between the onset of small-world behavior (quantified by small diameter and large clustering coefficients) and the transition from Poisson to GOE statistics (quantified by Brody parameter). We also present our analysis for a protein-protein interaction network in budding yeast.