Spatial-temporal dynamics of a Lotka-Volterra competition model with nonlocal dispersal under shifting environment

讲座时间 Datetime: 

星期五, 2019/07/05 - 从 16:30 到 17:30

地点 Venue: 

海滨红楼6号楼1楼会议室

报告人 Speaker: 

邹幸福 教授

单位 Affiliation: 

加拿⼤西安⼤略⼤学

报告摘要 Abstract: 

We consider a competitive system with nonlocal dispersals  in a 1-dimensional environment that is worsening with a constant speed, reflected by two shifting growth functions.  By analyzing the spatial-temporal dynamics of the model system,  we are able to identify certain ranges for the worsening speed $c$, respectively for (i)  extinction of both species; (ii) extinction of one species but persistence of the other; (iii) persistence of both species.  In the case of persistence of a species,  it is achieved through spreading to the direction of favourable environment  with certain speed(s), and some estimates of these speeds are also obtained. We also present some numeric simulation results which confirm our theoretical results, and in the mean time, motivate some challenging problems for future work.                

我们考虑在一维环境中具有非局部扩散的竞争系统，该系统以恒定速度恶化，由两个变化的增长函数反映。通过分析模型系统的时空动态，我们能够确定由恶化速度$c$变化引起的三种现象（i）两种物种都灭绝；（ii）一种物种灭绝，另一种物种持久生存；（iii）两种物种持久生存。在一个物种持久存在的情况下，它是通过以一定的速度向有利环境的方向传播来实现的，并且也得到了这些速度的一些估计。同时给出了一些数值模拟结果，证实了理论计算的正确性，同时也为今后的工作提出了一些具有挑战性的问题。