Comparison on Zhang neural dynamics and gradient-based neural dynamics for online solution of nonlinear time-varying equation
Different from gradient-based neural dynamics, a special kind of recurrent neural dynamics has recently been proposed by Zhang etal. for solving online time-varying problems. Such a recurrent neural dynamics is designed based on an indefinite error-monitoring function instead of a usually norm- or square-based energy function. In addition, Zhang neural dynamics (ZND) are depicted generally in implicit dynamics, whereas gradient-based neural dynamics (GND) are associated with explicit dynamics. In this paper, we generalize the ZND design method to solving online nonlinear time-varying equations in the form of f (x, t)=0. For comparative purposes, the GND model is also employed for such time-varying equations solving. Computer-simulation results via power-sigmoid activation functions substantiate the theoretical analysis and efficacy of the ZND model for solving online nonlinear time-varying equations.
gradient-based neural dynamics recurrent neural networks time-varying nonlinear equations exponential convergence