pth moment exponential stability of stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays

In this paper, stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are investigated. By using Lyapunov function and the Ito differential formula, some sufficient conditions for the pth moment exponential stability of such stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are established. An example is given to illustrate the feasibility of our main theoretical findings. Finally, the paper ends with a brief conclusion. Methodology and achieved results is to be presented

Further analysis of stability of uncertain neural networks with multiple time delays

This paper studies the robust stability of uncertain neural networks with multiple time delays with respect to the class of nondecreasing activation functions. By using the Lyapunov functional and homeomorphism mapping theorems, we derive a new delay-independent sufficient condition the existence, uniqueness, and global asymptotic stability of the equilibrium point for delayed neural networks with uncertain network parameters. The condition obtained for the robust stability establishes a matrix-norm relationship between the network parameters of the neural system, and therefore it can easily be verified. We also present some constructive numerical examples to compare the proposed result with results in the previously published corresponding literature. These comparative examples show that our new condition can be considered as an alternative result to the previous corresponding literature results as it defines a new set of network parameters ensuring the robust stability of delayed neural networks.Publisher's Versio

A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.In this Letter, the analysis problem for the existence and stability of periodic solutions is investigated for a class of general discrete-time recurrent neural networks with time-varying delays. For the neural networks under study, a generalized activation function is considered, and the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By employing the latest free-weighting matrix method, an appropriate Lyapunov–Krasovskii functional is constructed and several sufficient conditions are established to ensure the existence, uniqueness, and globally exponential stability of the periodic solution for the addressed neural network. The conditions are dependent on both the lower bound and upper bound of the time-varying time delays. Furthermore, the conditions are expressed in terms of the linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Two simulation examples are given to show the effectiveness and less conservatism of the proposed criteria.This work was supported in part by the National Natural Science Foundation of China under Grant 50608072, an International Joint Project sponsored by the Royal Society of the UK and the National Natural Science Foundation of China, and the Alexander von Humboldt Foundation of Germany

New synchronization criteria for an array of neural networks with hybrid coupling and time-varying delays

This paper is concerned with the global exponential synchronization for an array of hybrid coupled neural networks with time-varying leakage delay, discrete and distributed delays. Applying a novel Lyapunov functional and the property of outer coupling matrices of the neural networks, sufficient conditions are obtained for the global exponential synchronization of the system. The derived synchronization criteria are closely related with the time-varying delays and the coupling structure of the networks. The maximal allowable upper bounds of the time-varying delays can be obtained guaranteeing the global synchronization for the neural networks. The method we adopt in this paper is different from the commonly used linear matrix inequality (LMI) technique, and our synchronization conditions are new, which are easy to check in comparison with the previously reported LMI-based ones. Some examples are given to show the effectiveness of the obtained theoretical results

ψ-type stability of reaction–diffusion neural networks with time-varying discrete delays and bounded distributed delays

In this paper, the ψ-type stability and robust ψ-type stability for reaction–diffusion neural networks (RDNNs) with Dirichlet boundary conditions, time-varying discrete delays and bounded distributed delays are investigated, respectively. Firstly, we analyze the ψ-type stability and robust ψ-type stability of RDNNs with time-varying discrete delays by means of ψ-type functions combined with some inequality techniques, and put forward several ψ-type stability criteria for the considered networks. Additionally, the models of RDNNs with bounded distributed delays are established and some sufficient conditions to guarantee the ψ-type stability and robust ψ-type stability are given. Lastly, two examples are provided to confirm the effectiveness of the derived results

Finite-time Anti-synchronization of Memristive Stochastic BAM Neural Networks with Probabilistic Time-varying Delays

This paper investigates the drive-response finite-time anti-synchronization for memristive bidirectional associative memory neural networks (MBAMNNs). Firstly, a class of MBAMNNs with mixed probabilistic time-varying delays and stochastic perturbations is first formulated and analyzed in this paper. Secondly, an nonlinear control law is constructed and utilized to guarantee drive-response finite-time anti-synchronization of the neural networks. Thirdly, by employing some inequality technique and constructing an appropriate Lyapunov function, some anti-synchronization criteria are derived. Finally, a number simulation is provided to demonstrate the effectiveness of the proposed mechanism

Global Robust Exponential Stability and Periodic Solutions for Interval Cohen-Grossberg Neural Networks with Mixed Delays

A class of interval Cohen-Grossberg neural networks with time-varying delays and infinite distributed delays is investigated. By employing H-matrix and M-matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions are established for the existence, uniqueness, and global robust exponential stability of the equilibrium point and the periodic solution to the neural networks. Our results improve some previously published ones. Finally, numerical examples are given to illustrate the feasibility of the theoretical results and further to exhibit that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system admits rich and complex dynamics

Anti-periodic solution for fuzzy Cohen–Grossberg neural networks with time-varying and distributed delays

In this paper, by using a continuation theorem of coincidence degree theory and a differential inequality, we establish some sufficient conditions ensuring the existence and global exponential stability of anti-periodic solutions for a class of fuzzy Cohen–Grossberg neural networks with time-varying and distributed delays. In addition, we present an illustrative example to show the feasibility of obtained results

General decay lag anti-synchronization of multi-weighted delayed coupled neural networks with reaction–diffusion terms

We propose a new anti-synchronization concept, called general decay lag anti-synchronization, by combining the definitions of decay synchronization and lag synchronization. Novel criteria for the decay lag anti-synchronization of multi-weighted delayed coupled reaction–diffusion neural networks (MWDCRDNNs) with and without bounded distributed delays are derived by constructing an appropriate nonlinear controller and using the Lyapunov functional method. Moreover, the robust decay lag anti-synchronization of MWDCRDNNs with and without bounded distributed delays is considered. Finally, two numerical simulations are performed to validate the obtained results