Comprehensive study on complex-valued ZNN models activated by novel nonlinear functions for dynamic complex linear equations

This paper proposes two complex-valued zeroing neural network (Cv-ZNN) models for solving dynamic complex time-variant linear equations. The models involve two complex-valued nonlinear processing methods and adapt two real-valued activation functions. The convergence and robustness of the two Cv-ZNN models are analyzed comprehensively. Firstly, the convergence discussion shows that the corresponding stable error can rapidly converge to zero in finite time, with the upper limit of constriction time calculated. The upper limit of stable error is successfully obtained when the model implementation error is injected into the Cv-ZNN models, which displays their superior robustness. Besides, the results of numerical simulations reveal that the Cv-ZNN models effectively address the time-variant linear system of equations over complex field, even in noisy environments. The simulation results also demonstrate that two novel nonlinear activation functions perform much better than the Linear, Power, Bipolar Sigmoid Power-Sigmoid and Sign-bi-power activation functions.