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In this article artificial neural network (ANN) is used to estimate parameters of stochastic differential equations (SDEs) given the discrete output variables of the equations. Some techniques are used to improve ANN performance i...
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In this article artificial neural network (ANN) is used to estimate parameters of stochastic differential equations (SDEs) given the discrete output variables of the equations. Some techniques are used to improve ANN performance in data preparation and ANN training procedure. In particular, an increase in the number of Wiener processes used to create training data set raises the accuracy of estimates significantly. The analysis of the results suggests that ANN can predict parameters of SDEs accurately under certain noise level regimes using an appropriate network architecture.
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The study of uncertainty and its effect on information diffusion have become a recent problem in social network analysis. Contact rates between the social network users are not constant. There exist uncertainty in user's interest ...
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The study of uncertainty and its effect on information diffusion have become a recent problem in social network analysis. Contact rates between the social network users are not constant. There exist uncertainty in user's interest due to incomplete knowledge about others and stochastic properties present in user behavior. Keeping given this fact, we introduce a rumor model in a homogeneously mixed population on a social network including expert intervention. We also studied the stochastic version of the proposed model including fluctuations in contact rates. We ascertained a threshold known as basic influence number, R-0 and R-0 for deterministic and stochastic model respectively. We acquired the condition of local and global asymptotic stability of rumor free equilibrium respectively for the deterministic and stochastic model. Moreover, the mathematical state of epidemic invasion was obtained for the stochastic version of the model. Here, we conclude that epidemic can still grow in the presence of fluctuations (R-0 > 1) even when there is no epidemic invasion in the deterministic case (R-0 < 1). So a diffusion rate can be a cause of transient epidemic advance. (C) 2018 Elsevier B.V. All rights reserved.
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The dynamic properties of a class of neural networks (which includes the Hopfield model as a special case) are investigated by studying the qualitative behavior of equilibrium points. The results fall into one of two categories: r...
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The dynamic properties of a class of neural networks (which includes the Hopfield model as a special case) are investigated by studying the qualitative behavior of equilibrium points. The results fall into one of two categories: results pertaining to analysis (e.g., stability properties of an equilibrium, asymptotic behavior of solutions, etc.) and results pertaining to synthesis (e.g. the design of a neural network with prespecified equilibrium points which are asymptotically stable). Most (but not all) of the results presented are global, and their applicability is demonstrated by an example.
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In this paper, the mean-square exponential stabilization for stochastic differential equations with Markovian switching is studied. Specifically, a new set of sufficient conditions is derived to obtain the aperiodically intermitte...
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In this paper, the mean-square exponential stabilization for stochastic differential equations with Markovian switching is studied. Specifically, a new set of sufficient conditions is derived to obtain the aperiodically intermittent control design which exponentially stabilizes the addressed hybrid stochastic differential equations. Further, stabilization problem by periodically intermittent control can be deduced as a special case from the developed results. As an application, we consider the Hopfield neutral network model with simulations to illustrate the effectiveness of developed aperiodically intermittent control design. (c) 2020 Elsevier Ltd. All rights reserved.
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Estimates of exponential convergence rate and exponential stability are studied for a class of neural networks which includes Hopfield neural networks and cellular neural networks. Both local and global exponential convergence are...
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Estimates of exponential convergence rate and exponential stability are studied for a class of neural networks which includes Hopfield neural networks and cellular neural networks. Both local and global exponential convergence are discussed. Theorems for estimation of the exponential convergence rate are established and the bounds on the rate of convergence are given. The domains of attraction in the case of local exponential convergence are obtained. Simple conditions are presented for checking exponential stability of the neural networks.
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In this paper, the two-step Maruyama methods of stochastic delay Hopfield neural networks are studied. We have found that under what choices of step-size, the two-step Maruyama methods of stochastic delay Hopfield networks, mainta...
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In this paper, the two-step Maruyama methods of stochastic delay Hopfield neural networks are studied. We have found that under what choices of step-size, the two-step Maruyama methods of stochastic delay Hopfield networks, maintain the stability of exact solutions. The mean-square stability of two-step Maruyama methods of stochastic delay Hopfield neural networks is investigated under suitable conditions. Also, the almost sure exponential stability of two-step Maruyama methods of stochastic delay Hopfield networks is proved using the semi-martingale convergence theorem. Further, the comparisons of stability conditions to the previous results in Liu and Zhu (2015), Rathinasamy (2012) and Ronghua et al. (2010) are given. Numerical experiments are provided to illustrate our theoretical results. (C) 2018 Elsevier Inc. All rights reserved.
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Both exponential and stochastic stabilities of the Hopfield neural network are analyzed. The results are especially useful for analyzing the stabilities of asymmetric neural networks. A constraint on the connection matrix has been...
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Both exponential and stochastic stabilities of the Hopfield neural network are analyzed. The results are especially useful for analyzing the stabilities of asymmetric neural networks. A constraint on the connection matrix has been found under which the neural network has a unique and exponentially stable equilibrium. Given any connection matrix, this constraint can be satisfied through the adjustment of the gains of the amplifiers and the resistances in the neural net circuit. A one-to-one and smooth map between input currents and the equilibria of the neural network can be set up. The above results can be applied to the master/slave net to prove that the master net can find the best connection matrix for the slave net. For the neural network disturbed by some noise, the stochastic stability of the network is also analyzed. A special asymmetric neural network formed by a closed chain of formal neurons is also studied for its stability and oscillation. Both stable and oscillatory dynamics are obtained in the closed chain network through the adjustment of the gains and resistances of the amplifiers.
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This brief is concerned with the analysis problem of global exponential stability in the mean square sense for a class of linear discrete-time recurrent neural networks (DRNNs) with stochastic delay. Different from the prior resea...
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This brief is concerned with the analysis problem of global exponential stability in the mean square sense for a class of linear discrete-time recurrent neural networks (DRNNs) with stochastic delay. Different from the prior research works, the effects of
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This article is devoted to the existence and the global stability of stationary solutions for stochastic Hopfield neural networks with time delays and additive white noises. Using the method of random dynamical systems, we present...
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This article is devoted to the existence and the global stability of stationary solutions for stochastic Hopfield neural networks with time delays and additive white noises. Using the method of random dynamical systems, we present a new approach to guarantee that the infinite-dimensional stochastic flow generated by stochastic delay differential equations admits a globally attracting random equilibrium in the state-space of continuous functions. An example is given to illustrate the effectiveness of our results, and the forward trajectory synchronization will occur.
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Recently the investigation on the stability of the numerical solutions to delayed stochastic differential equations has received an increasing attention, but there has been little work on the stability analysis of the numerical so...
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Recently the investigation on the stability of the numerical solutions to delayed stochastic differential equations has received an increasing attention, but there has been little work on the stability analysis of the numerical solutions to delayed stochastic Hopfield neural networks (DSHNNs) so far. The aim in this paper is to study the mean square exponential stability of the split-step theta (SST) method and the stochastic linear theta (SLT) method for the underlying model. It is proved that, for any theta is an element of [0, 1/2), there exists a constant Delta* > 0 depending on theta such that the numerical schemes produced by the SST method and the SLT method are mean square exponentially stable for Delta is an element of(0, Delta*), under the same assumptions as those to guarantee the mean square exponential stability of the underlying continuous model. For the case theta is an element of [1/2, 1], we show the same stability conclusion for all Delta > 0. To carry out the required conclusion, a novel technique for the stability analysis of discrete numerical schemes with multi time delays, namely the weighted sum Lyapunov functional method, is proposed. Finally, a numerical example is given to illustrate the application of the suggested methods and to verify the stability conclusions obtained. (C) 2018 Elsevier B.V. All rights reserved.
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