Discrete the solving model of time-variant standard Sylvester-conjugate matrix equations using Euler-forward formula

TL;DR

This paper introduces discrete models for time-variant Sylvester-conjugate matrix equations using Euler-forward discretization, highlighting differences from continuous models in neural dynamics and convergence behavior.

Contribution

It proposes novel discrete models based on Euler-forward formula for solving time-variant Sylvester-conjugate matrix equations, addressing practical computational needs.

Findings

Discrete models show different neural dynamics from continuous models.

Step size affects convergence and neural trajectory correction.

Discretization impacts sampling errors and space approximation in neural systems.

Abstract

Time-variant standard Sylvester-conjugate matrix equations are presented as early time-variant versions of the complex conjugate matrix equations. Current solving methods include Con-CZND1 and Con-CZND2 models, both of which use ode45 for continuous model. Given practical computational considerations, discrete these models is also important. Based on Euler-forward formula discretion, Con-DZND1-2i model and Con-DZND2-2i model are proposed. Numerical experiments using step sizes of 0.1 and 0.001. The above experiments show that Con-DZND1-2i model and Con-DZND2-2i model exhibit different neural dynamics compared to their continuous counterparts, such as trajectory correction in Con-DZND2-2i model and the swallowing phenomenon in Con-DZND1-2i model, with convergence affected by step size. These experiments highlight the differences between optimizing sampling discretion errors and space compressive approximation errors in neural dynamics.