Bidirectional associative memories
IEEE Transactions on Systems, Man and Cybernetics
A discrete model of competition
Mathematics and Computers in Simulation
Dynamics of a class of discete-time neural networks and their comtinuous-time counterparts
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
Computer simulations of exponentially convergent networks with large impulses
Mathematics and Computers in Simulation
A unified treatment for stability preservation in computer simulations of impulsive BAM networks
Computers & Mathematics with Applications
Exponential Stability of Discrete-Time Cohen-Grossberg Neural Networks with Delays
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks
The numerical simulation of periodic solutions for a neural network
Computers & Mathematics with Applications
Neural Processing Letters
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Numerical simulation of periodic solutions for a class of numerical discretization neural networks
Mathematical and Computer Modelling: An International Journal
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We formulate discrete-time analogues of integrodifferential equations modelling bidirectional neural networks studied by Gopalsamy and He. The discrete-time analogues are considered to be numerical discretizations of the continuous-time networks and we study their dynamical characteristics. It is shown that the discrete-time analogues preserve the equilibria of the continuous-time networks. By constructing a Lyapunov-type sequence, we obtain easily verifiable sufficient conditions under which every solution of the discrete-time analogue converges exponentially to the unique equilibrium. The sufficient conditions are identical to those obtained by Gopalsamy and He for the uniqueness and global asymptotic stability of the equilibrium of the continuous-time network. By constructing discrete-time versions of Halanay-type inequalities, we obtain another set of easily verifiable sufficient conditions for the global exponential stability of the unique equilibrium of the discrete-time analogue. The latter sufficient conditions have not been obtained in the literature of continuous-time bidirectional neural networks. Several computer simulations are provided to illustrate the advantages of our discrete-time analogue in numerically simulating the continuous-time network with distributed delays over finite intervals.