Stability analysis for nonlinear multi-variable delay perturbation problems

摘要

This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems (MVDPP) of the form x'(t) = f(x(t) , x(t - τ_1, (t)) ,..., x(t - τ_m(t)), y(t), y(t - τ_1 (t)),..., y( t - τ_m(t))), and εy'(t) = g(x(t), x(t - τ_1(t)),..., x(t - τ_m(t)), y(t),y(t - τ_1 (t)),... , y( t - τ_m(t))), where 0 < ε 1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.