Analyzing stability of a delay differential equation involving two delays

Abstract

Analysis of the systems involving delay is a popular topic among applied scientists. In the present work, we analyze the generalized equation $D^{\alpha }x(t)=g\left(x(t-{\tau }_1),x(t-{\tau }_2)\right)$ involving two delays viz. ${\tau }_1\ge 0$ and ${\tau }_2\ge 0$. We use the the 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.

10 pages, 7 figures