# American Institute of Mathematical Sciences

June  2018, 23(4): 1559-1579. doi: 10.3934/dcdsb.2018059

## Dynamics of a Lotka-Volterra competition-diffusion model with stage structure and spatial heterogeneity

 1 College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China 2 Department of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China

* Corresponding author: S. Guo

Received  April 2017 Revised  August 2017 Published  February 2018

Fund Project: The second author is supported by NSF of China (Grants No. 11671123)

This paper is concerned with a Lotka-Volterra competition-diffusion model with stage structure and spatial heterogeneity. By analyzing the sign of the principal eigenvalue corresponding to each semi-trivial solution, we obtain the linear stability and global attractivity of the semi-trivial solution. In addition, an attracting region was obtained by means of the method of upper and lower solutions.

Citation: Shuling Yan, Shangjiang Guo. Dynamics of a Lotka-Volterra competition-diffusion model with stage structure and spatial heterogeneity. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1559-1579. doi: 10.3934/dcdsb.2018059
##### References:

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##### References:
Solutions of model (7) with $\tau = 0.3<\tau_*$ tend to the semi-trivial steady state solution $(\theta_{d_1,\alpha,0},0)$.
Solutions of model (7) with $\tau = 3>\tau^*$ tend to the semi-trivial steady state solution $(0, \theta_{d_2,r})$.
Solutions of model (7) with $\tau = 1.485\in(\ln\dfrac{c\bar{\alpha}}{\bar{r}}, \ln\dfrac{\bar{\alpha}}{a\bar{r}})$ tend to a positive steady state.
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