Discrete-time analogues of integrodifferential equations modeling neural networks

Discrete-time analogues of integrodifferential equations modeling neural networks with periodic inputs are introduced. 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 periodicity of the continuous-time networks. By constructing a Lyapunov-type sequence, we obtain easily verifiable sufficient conditions ensuring that every solutions of the discrete-time analogue converge exponentially to the unique periodic solutions.