Analyzing stability of a delay differential equation involving two delays

Analysis of the systems involving delay is a popular topic among applied scientists. In the present work, we analyze the generalized equation $D^α x(t) = g\left(x(t-τ_1), x(t-τ_2)\right)$ involving two delays viz. $τ_1\geq 0$ and $τ_2\geq 0$. 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.

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