Stability and bifurcation analysis of a generalized scalar delay differential equation

Abstract

This paper deals with the stability and bifurcation analysis of a general form of equation Dαx(t) = g(x(t), x(t-τ) involving the derivative of order α ε{lunate} (0, 1] and a constant delay τ ≥ 0. The stability of equilibrium points is presented in terms of the stability regions and critical surfaces. We provide a necessary condition to exist chaos in the system also. A wide range of delay differential equations involving a constant delay can be analyzed using the results proposed in this paper. The illustrative examples are provided to explain the theory.