243 research outputs found
Exponential Lag Synchronization of Cohen-Grossberg Neural Networks with Discrete and Distributed Delays on Time Scales
In this article, we investigate exponential lag synchronization results for
the Cohen-Grossberg neural networks (C-GNNs) with discrete and distributed
delays on an arbitrary time domain by applying feedback control. We formulate
the problem by using the time scales theory so that the results can be applied
to any uniform or non-uniform time domains. Also, we provide a comparison of
results that shows that obtained results are unified and generalize the
existing results. Mainly, we use the unified matrix-measure theory and Halanay
inequality to establish these results. In the last section, we provide two
simulated examples for different time domains to show the effectiveness and
generality of the obtained analytical results.Comment: 20 pages, 18 figure
Generalized non-autonomous Cohen-Grossberg neural network model
In the present paper, we investigate both the global exponential stability
and the existence of a periodic solution of a general differential equation
with unbounded distributed delays. The main stability criterion depends on the
dominance of the non-delay terms over the delay terms. The criterion for the
existence of a periodic solution is obtained with the application of the
coincide degree theorem. We use the main results to get criteria for the
existence and global exponential stability of periodic solutions of a
generalized higher-order periodic Cohen-Grossberg neural network model with
discrete-time varying delays and infinite distributed delays. Additionally, we
provide a comparison with the results in the literature and a numerical
simulation to illustrate the effectiveness of some of our results.Comment: 30 page
Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays
Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we introduce a new class of discrete-time neural networks (DNNs) with Markovian jumping parameters as well as mode-dependent mixed time delays (both discrete and distributed time delays). Specifically, the parameters of the DNNs are subject to the switching from one to another at different times according to a Markov chain, and the mixed time delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. We first deal with the stability analysis problem of the addressed neural networks. A special inequality is developed to account for the mixed time delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the stochastic stability. We then turn to the synchronization problem among an array of identical coupled Markovian jumping neural networks with mixed mode-dependent time delays. By utilizing the Lyapunov stability theory and the Kronecker product, it is shown that the addressed synchronization problem is solvable if several LMIs are feasible. Hence, different from the commonly used matrix norm theories (such as the M-matrix method), a unified LMI approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation, where the LMIs can be easily solved by using the available Matlab LMI toolbox. Two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained
Cohen-Grossberg neural networks with unpredictable and Poisson stable dynamics
In this paper, Cohen-Grossberg neural networks with unpredictable and
compartmental periodic unpredictable strengths of connectivity between cells
and inputs are investigated. To approve Poisson stability and unpredictability
in neural networks, the method of included intervals and contraction mapping
principle are used. The existence, uniqueness, and exponential stability of
unpredictable and Poisson stable outputs are discussed. Examples with numerical
simulations that support the theoretical results are provided. The dependence
of the neural network dynamics on the numerical characteristic, the degree of
periodicity, is shown
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