Analysis of a Class of Two-delay Fractional Differential Equation

Abstract

The differential equations involving two discrete delays are helpful in modeling two different processes in one model. We provide the stability and bifurcation analysis in the fractional order delay differential equation $D^\alpha x(t)=a x(t)+b x(t-\tau)-b x(t-2\tau)$ in the $ab$-plane. Various regions of stability include stable (S), unstable (U), single stable region (SSR), and stability switch (SS). In the stable region, the system is stable for all the delay values. The region SSR has a critical value of delay that bifurcates the stable and unstable behavior. Switching of stable and unstable behaviors is observed in the SS region.