Stability and Bifurcation Analysis of a Discrete Gompertz Model with Time Delay
نویسنده
چکیده
In this paper, we consider a discrete Gompertz model with time delay. Firstly, the stability of the equilibrium of the system is investigated by analyzing the characteristic equation. By choosing the time delay as a bifurcation parameter, we prove that NeimarkSacker bifurcations occur when the delay passes a sequence of critical values. The direction and stability of the Neimark-Sacker are determined by using normal forms and centre manifold theory. Finally, some numerical simulations are given to verify the theoretical analysis. Keywords—Gompertz system; Neimark-Sacker bifurcation; Stability; Time delay.
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