Analysing the stability of a delay differential equation involving two delays

Abstract

Analysis of systems involving delay is a popular topic among the applied scientists. In the present work, we analyse the generalised equation Dαx(t) = g(x(t- τ1) , x(t- τ2)) involving two delays, viz. τ1≥ 0 and τ2≥ 0. We use stability conditions to propose the critical values of delays. Using examples, we show that the chaotic oscillations are observed in the unstable region only. We also propose a numerical scheme to solve such equations.