# American Institute of Mathematical Sciences

## Dirichlet problem for a diffusive logistic population model with two delays

 1 Tongji Zhejiang College, Jiaxing, Zhejiang 314051, China 2 School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China 3 Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada

* Corresponding author

Received  December 2018 Revised  February 2019 Published  November 2019

In this paper, we investigate a diffusive logistic equation with non-zero Dirichlet boundary condition and two delays. We first exclude the existence of positive heterogeneous steady states, which implies the uniqueness of constant positive steady state. Then, we analyze the local stability and local Hopf bifurcation at the positive steady state. We show that multiple delays can induce multiple stability switches. Furthermore, we prove global stability of the positive steady state under certain conditions and obtain global Hopf bifurcation results. Our theoretical results are illustrated with numerical simulations.

Citation: Xuejun Pan, Hongying Shu, Yuming Chen. Dirichlet problem for a diffusive logistic population model with two delays. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020134
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##### References:
The phase portrait of (9)
The root distribution of (14)
Left: $u_*$ is stable at $\tau = 5$. Right: $u_*$ is unstable at $\tau = 12$
Left: $u_*$ is stable at $\tau = 18$. Right: $u_*$ is unstable at $\tau = 30$
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