Stability and Bifurcation Analysis of a Nonlinear Discrete Logistic Model with Delay

Abstract EN

We consider a nonlinear discrete logistic model with delay.

The characteristic equation of the linearized system at the positive equilibrium is a polynomial equation involving high order terms.

We obtain the conditions ensuring the asymptotic stability of the positive equilibrium and the existence of Neimark-Sacker bifurcation, with respect to the parameter of the model.

Based on the bifurcation theory, we discuss Neimark-Sacker bifurcation direction and the stability of bifurcated solutions.

Finally, some numerical simulations are performed to illustrate the theoretical results.