750 research outputs found

    Chaos and Asymptotical Stability in Discrete-time Neural Networks

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    This paper aims to theoretically prove by applying Marotto's Theorem that both transiently chaotic neural networks (TCNN) and discrete-time recurrent neural networks (DRNN) have chaotic structure. A significant property of TCNN and DRNN is that they have only one fixed point, when absolute values of the self-feedback connection weights in TCNN and the difference time in DRNN are sufficiently large. We show that this unique fixed point can actually evolve into a snap-back repeller which generates chaotic structure, if several conditions are satisfied. On the other hand, by using the Lyapunov functions, we also derive sufficient conditions on asymptotical stability for symmetrical versions of both TCNN and DRNN, under which TCNN and DRNN asymptotically converge to a fixed point. Furthermore, generic bifurcations are also considered in this paper. Since both of TCNN and DRNN are not special but simple and general, the obtained theoretical results hold for a wide class of discrete-time neural networks. To demonstrate the theoretical results of this paper better, several numerical simulations are provided as illustrating examples.Comment: This paper will be published in Physica D. Figures should be requested to the first autho

    Probing the dynamics of identified neurons with a data-driven modeling approach

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    In controlling animal behavior the nervous system has to perform within the operational limits set by the requirements of each specific behavior. The implications for the corresponding range of suitable network, single neuron, and ion channel properties have remained elusive. In this article we approach the question of how well-constrained properties of neuronal systems may be on the neuronal level. We used large data sets of the activity of isolated invertebrate identified cells and built an accurate conductance-based model for this cell type using customized automated parameter estimation techniques. By direct inspection of the data we found that the variability of the neurons is larger when they are isolated from the circuit than when in the intact system. Furthermore, the responses of the neurons to perturbations appear to be more consistent than their autonomous behavior under stationary conditions. In the developed model, the constraints on different parameters that enforce appropriate model dynamics vary widely from some very tightly controlled parameters to others that are almost arbitrary. The model also allows predictions for the effect of blocking selected ionic currents and to prove that the origin of irregular dynamics in the neuron model is proper chaoticity and that this chaoticity is typical in an appropriate sense. Our results indicate that data driven models are useful tools for the in-depth analysis of neuronal dynamics. The better consistency of responses to perturbations, in the real neurons as well as in the model, suggests a paradigm shift away from measuring autonomous dynamics alone towards protocols of controlled perturbations. Our predictions for the impact of channel blockers on the neuronal dynamics and the proof of chaoticity underscore the wide scope of our approach

    Hopf Bifurcation and Chaos in a Single Inertial Neuron Model with Time Delay

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    A delayed differential equation modelling a single neuron with inertial term is considered in this paper. Hopf bifurcation is studied by using the normal form theory of retarded functional differential equations. When adopting a nonmonotonic activation function, chaotic behavior is observed. Phase plots, waveform plots, and power spectra are presented to confirm the chaoticity.Comment: 12 pages, 7 figure

    Chaotic Neural Network with Radial Basis Function Disturbance

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    This novel chaotic neural network bases on the Chen’s transiently chaotic neural network. It is proposed by introducing radial basis function as disturbance item into the inside state. Analyze the dynamics behavior of the single chaotic neuron and the chaotic search capability of the network. Research the capability of the novel network for resisting the disturbance. This chaotic neural network with radial basis function disturbance is used to solve TSP. The simulation result indicates that this network can avoid the limit of being trapped into the local minima and the capability of resisting the disturbance is perfect

    Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis

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    We show how the Equation-Free approach for multi-scale computations can be exploited to systematically study the dynamics of neural interactions on a random regular connected graph under a pairwise representation perspective. Using an individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of simulated annealing we compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level. We also exploit the scheme to perform a rare-events analysis by estimating an effective Fokker-Planck describing the evolving probability density function of the corresponding coarse-grained observables
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