Zhang dynamics with modified error-functions for online solution of nonlinear equations so as to avoid local minima

Our previous work shows the efficacy and better performance of the Zhang dynamics (ZD) model for solving online nonlinear equations, as compared with the conventional gradient dynamics (GD) model. It is also discovered that, if a nonlinear equation possesses a local minimum point, the ZD state, starting from some initial value close to it, may move towards the local minimum point and then stop with warning information. In comparison, the GD state falls into the local minimum point (with no warning). Inspired by Wu's work, we improve the ZD model by defining two modified error-functions and generating new neural-dynamic forms to overcome such a local-minimum problem. Computer-simulation results further demonstrate the novelty and efficacy of the proposed ZD models (activated by power-sigmoid functions) with two new modified error-functions on the online solution of nonlinear equations involving local minima.