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

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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.

## Keywords

Recurrent neural networks Gradient-based neural dynamics Time-varying nonlinear equations Exponential convergence## Notes

### Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grants 61075121, 60935001 and 60775050, and also by the Fundamental Research Funds for the Central Universities of China.

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