An efficient zeroing neural network for solving time-varying nonlinear equations

Defining efficient families of recurrent neural networks (RNN) models for solving time-varying nonlinear equations is an interesting research topic in applied mathematics. Accordingly, one of the underlying elements in designing RNN is the use of efficient nonlinear activation functions. The role of the activation function is to bring out an output from a set of input values that are supplied into a node. Our goal is to define new family of activation functions consisting of a fixed gain parameter and a functional part. Corresponding zeroing neural networks (ZNN) is defined, termed as varying-parameter improved zeroing neural network (VPIZNN), and applied to solving time-varying nonlinear equations. Compared with previous ZNN models, the new VPIZNN models reach an accelerated finite-time convergence due to the new time-varying activation function which is embedded into the VPIZNN design. Theoretical results and numerical experiments are presented to demonstrate the superiority of the novel VPIZNN formula. The capability of the proposed VPIZNN models are demonstrated in studying and solving the Van der Pol equation and finding the root (m)va(t).