Convergence and stability results of Zhang neural network solving systems of time-varying nonlinear equations

Abstract

For solving systems of time-varying nonlinear equations, this paper generalizes a special kind of recurrent neural network by using a design method proposed by Zhang et al. Such a recurrent neural network (termed Zhang neural network, ZNN) is designed based on an indefinite error-function instead of a norm-based energy function. Theoretical analysis and results of convergence and stability are presented to show the desirable properties (e.g., large-scale exponential convergence) of ZNN via two different activation-function arrays for solving systems of time-varying nonlinear equations. Computer-simulation results substantiate further the theoretical analysis and efficacy of ZNN for solving systems of time-varying nonlinear equations.