Analysing the stability of a delay differential equation involving two delays

[摘要] Analysis of systems involving delay is a popular topic among the applied scientists. In the present work, we analyse the generalised equation $D^{\alpha}x(t) = g(x(t − \tau_{1}), x(t − \tau_{2}))$ involving two delays, viz. $\tau_{1} \geq 0$ and $\tau_{2} \geq 0$. 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.

[学科分类] 物理（综合）

[关键词] Fractional order;chaos;multiple delay;stability