Comparison on Zhang neural dynamics and gradient-based neural dynamics for online solution of nonlinear time-varying equation

Authors:
Yunong Zhang;Chenfu Yi;Dongsheng Guo;Jinhuan Zheng
Affiliations:
Sun Yat-sen University, School of Information Science and Technology, 510006, Guangzhou, China;Sun Yat-sen University, School of Information Science and Technology, 510006, Guangzhou, China and Jiangxi University of Science and Technology, School of Information Engineering, 341000, Ganzhou, ...;Sun Yat-sen University, School of Information Science and Technology, 510006, Guangzhou, China;Sun Yat-sen University, School of Software, 510006, Guangzhou, China
Venue:
Neural Computing and Applications
Year:
2011

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Abstract

Different from gradient-based neural dynamics, a special kind of recurrent neural dynamics has recently been proposed by Zhang et al. 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.