Simply and effectively proved square characteristics of discrete-time zd solving systems of time-varying nonlinear equations

A special class of continuous-time neural dynamics termed Zhang dynamics (ZD) has been investigated and generalized for solving the systems of time-varying nonlinear equations (STVNE). For possible digital hardware realization, the discrete-time ZD (DTZD) models are presented and investigated in this paper for solving the STVNE in the form of f(x(t), t) = 0 ∈ ℝⁿ. For comparative purposes, the Newton iteration is also presented to solve the STVNE. Theoretical analysis, as simply and effectively proved, shows that the steady-state residual errors of the presented DTZD models are of O(τ²), which is further verified by the follow-up numerical experiments.