Finite-time solution to nonlinear equation using recurrent neural dynamics with a specially-constructed activation function

A recurrent neural dynamics (termed improved Zhang dynamics, IZD), together with a specially-constructed activation function, is proposed and investigated for finding the root of nonlinear equation in this paper. It is analyzed that the IZD model can converge to the theoretical solution within finite time. Besides, the upper bound of convergence time is estimated analytically. Compared with conventional gradient-based dynamics (GD), our proposed IZD model in the form of implicit dynamics has the following advantages: (1) has better consistency with actual situations; and (2) has a greater ability in representing dynamical systems. Besides, our model can achieve superior convergence performance (i.e., finite-time convergence) in comparison with the existing neural dynamics, specifically the original ZD (OZD) model. Both theoretical analysis and computer-simulation results substantiate the effectiveness and superiority of the IZD model for solving nonlinear equation in real-time.