On the dynamics of the singularly perturbed Riccati differential equation with two different delays

Abstract

In this paper, we consider the singularly perturbation of the Riccati difference equation with two different delays. At first, we study the local stability of the fixed points and its corresponding characteristic equation of the linearized system. At second, we show that there is Hopf bifurcation with restricted condition for occurrence. Then we get out the discretized system by applying the method of steps. Local stability and bifurcation analysis of the discretized system. We compare the results with the results of the Riccati differential equation with two different delays. Finally, numerical simulations including bifurcation diagram, Lyapunov exponent and phase portraits are carried out to confirm the analytical findings .