We present observational evidence from studies on primary cortical cultures from AD transgenic mice, APPSwe/PS1ΔE9 (APP/PS1) mice, for significant decrease in total spine density at DIV-15 and onward. This indicates reduction in potential healthy synapses and strength of connections among neurons. Based on this, a network model of neurons is developed, that explains the consequent loss of coordinated activity and transmission efficiency among neurons that manifests over time.
View Article and Find Full Text PDFTo model the dependence of extreme events on locations, we consider extreme events of Brownian particles in a potential. We find that barring the exception of very large potentials and/or very small regions, in general, the probability of extreme events increases with the potential. Our approach is general and can be useful for studying several complex systems.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
November 2015
We study the generalized synchronization and its stability using the master stability function (MSF) in a network of coupled nearly identical dynamical systems. We extend the MSF approach for the case of degenerate eigenvalues of the coupling matrix. Using the MSF we study the size instability in star and ring networks for coupled nearly identical dynamical systems.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
February 2014
We report the first experimental observation of extreme multistability in a controlled laboratory investigation. Extreme multistability arises when infinitely many attractors coexist for the same set of system parameters. The behavior was predicted earlier on theoretical grounds, supported by numerical studies of models of two coupled identical or nearly identical systems.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
May 2012
Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the context of complex networks. This was motivated by the occurrence of rare events such as traffic jams, floods, and power blackouts which take place on networks.
View Article and Find Full Text PDFWe investigate synchronization of time varying networks and stability conditions. We derive interesting relations between the critical coupling constants for synchronization and switching times for time-varying and time average networks. The relations are based on the additive property of Lyapunov exponents and are verified experimentally in electronic circuit.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
April 2012
We present a mechanism for amplitude death in coupled nonlinear dynamical systems on a complex network having interactions with a common environment like external system. We develop a general stability analysis that is valid for any network topology and obtain the threshold values of coupling constants for the onset of amplitude death. An important outcome of our study is a universal relation between the critical coupling strength and the largest nonzero eigenvalue of the coupling matrix.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
October 2011
We introduce a general mechanism for amplitude death in coupled synchronizable dynamical systems. It is known that when two systems are coupled directly, they can synchronize under suitable conditions. When an indirect feedback coupling through an environment or an external system is introduced in them, it is found to induce a tendency for antisynchronization.
View Article and Find Full Text PDFWe analyze the desynchronization bifurcation in the coupled Rössler oscillators. After the bifurcation the coupled oscillators move away from each other with a square root dependence on the parameter. We define system transverse Lyapunov exponents (STLE), and in the desynchronized state one is positive while the other is negative.
View Article and Find Full Text PDFA wide spectrum of extreme events ranging from traffic jams to floods take place on networks. Motivated by these, we employ a random walk model for transport and obtain analytical and numerical results for the extreme events on networks. They reveal an unforeseen, and yet a robust, feature: small degree nodes of a network are more likely to encounter extreme events than the hubs.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
April 2010
We consider synchronization of chaotic systems coupled indirectly through common environment where the environment has an intrinsic dynamics of its own modulated via feedback from the systems. We find that a rich variety of synchronization behavior, such as in-phase, antiphase, complete, and antisynchronization, is possible. We present an approximate stability analysis for the different synchronization behaviors.
View Article and Find Full Text PDFWe show that the existing methods for computing the f(alpha) spectrum from a time series can be improved by using a new algorithmic scheme. The scheme relies on the basic idea that the smooth convex profile of a typical f(alpha) spectrum can be fitted with an analytic function involving a set of four independent parameters. While the standard existing schemes [P.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
October 2009
A method based on a modified Newton-Raphson scheme is presented to estimate parameters of a nonlinear dynamical system from the time series data of the variables. The method removes some of the problems associated with the standard synchronization based methods. An important achievement of this method is that it is possible to determine the exact form of dynamical equations for systems with quadratic nonlinearity.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
May 2009
A method to synchronize two chaotic systems with anticipation or lag, coupled in the drive response mode, is proposed. The coupling involves variable delay with three time scales. The method has the advantage that synchronization is realized with intermittent information about the driving system at intervals fixed by a reset time.
View Article and Find Full Text PDFMore than 99% of the species that ever existed on the surface of the Earth are now extinct and their extinction on a global scale has been a puzzle. One may think that a species under an external threat may survive in some isolated locations leading to the revival of the species. Using a general model we show that, under a common external forcing, the species with a quadratic saturation term first undergoes spatial synchronization and then extinction.
View Article and Find Full Text PDFWe consider synchronization properties of coupled dynamics on time-varying networks and the corresponding time-average network. We find that if the different Laplacians corresponding to the time-varying networks commute with each other then the stability of the synchronized state for both the time-varying and the time-average topologies are approximately the same. On the other hand for noncommuting Laplacians the stability of the synchronized state for the time-varying topology is in general better than the time-average topology.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
July 2005
We study self-organized and driven synchronization in some simple coupled map networks, namely globally coupled networks and complete bipartite networks, using both linear stability analysis and Lyapunov function approach and determine stability conditions for synchronization. The phase diagrams for the networks studied here have features very similar to the different kinds of structurally similar networks studied in Part I. Lyapunov function approach shows that when any two nodes are in driven synchronization, all the coupling terms in the difference between the variables of these two nodes cancel out, whereas when they are in self-organized synchronization, the direct coupling term between the two nodes adds an extra term while the other couplings cancel out.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
July 2005
We study the synchronization of coupled maps on a variety of networks including regular one- and two-dimensional networks, scale-free networks, small world networks, tree networks, and random networks. For small coupling strengths nodes show turbulent behavior but form phase synchronized clusters as coupling increases. When nodes show synchronized behavior, we observe two interesting phenomena.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
August 2004
We propose a model of coupled random walks for stock-stock correlations. The walks in the model are coupled via a mechanism that the displacement (price change) of each walk (stock) is activated by the price gradients over some underlying network. We assume that the network has two underlying structures, describing the correlations among the stocks of the whole market and among those within individual groups, respectively, each with a coupling parameter controlling the degree of correlation.
View Article and Find Full Text PDFWe study the phase synchronization and cluster formation in coupled maps on different networks. We identify two different mechanisms of cluster formation: (a) self-organized phase synchronization which leads to clusters with dominant intracluster couplings and (b) driven phase synchronization which leads to clusters with dominant intercluster couplings. In the novel driven synchronization the nodes of one cluster are driven by those of the others.
View Article and Find Full Text PDFPhys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics
October 1999
A stochastic hierarchical model of cluster-cluster aggregation, which is obtained by introducing a sticking probability into the recently proposed hierarchical model by Sornsen and Oh [Phys. Rev. E 58, 7545 (1998)], is presented.
View Article and Find Full Text PDFPhys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics
August 1999
Recently, Watts and Strogatz [Nature (London) 393, 440 (1998)] offered an interesting model of small-world networks. Here we concretize the concept of a "faraway" connection in a network by defining a far edge. Our definition is algorithmic and independent of any external parameters such as topology of the underlying space of the network.
View Article and Find Full Text PDFPhys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics
June 1999
We investigate the nature of the transitions between free and self-trapping states occurring in systems described by augmented forms of the discrete nonlinear Schrödinger equation. These arise from an interaction between a moving quasiparticle (such as an electron or an exciton) and lattice vibrations, when the effects of nonlinearities in interaction potential and restoring force are included. We derive analytic conditions for the stability of the free state and the crossover between first- and second-order transitions.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
April 2001
We present analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from regular to random behavior with increasing distance from the starting point of the random walk. We introduce an independent step approximation, which enables us to obtain analytic results for the average access time.
View Article and Find Full Text PDFPhys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics
June 2000
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when the time series of a scalar function of the variables of the underlying dynamical system is given. We find that it is possible to obtain synchronization as well as parameter estimation using such a time series.
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