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Bifurcation Analysis for a Delayed Diffusive Logistic Population Model in the Advective Heterogeneous Environment
Journal of Dynamics and Differential Equations ( IF 1.3 ) Pub Date : 2019-03-08 , DOI: 10.1007/s10884-019-09739-0 Shanshan Chen , Junjie Wei , Xue Zhang
Journal of Dynamics and Differential Equations ( IF 1.3 ) Pub Date : 2019-03-08 , DOI: 10.1007/s10884-019-09739-0 Shanshan Chen , Junjie Wei , Xue Zhang
In this paper, we investigate a delayed reaction–diffusion–advection equation, which models the population dynamics in the advective heterogeneous environment. The existence of the nonconstant positive steady state and associated Hopf bifurcation are obtained. A weighted inner product associated with the advection rate is introduced to compute the normal forms, which is the main difference between Hopf bifurcation for delayed reaction–diffusion–advection model and that for delayed reaction–diffusion model. Moreover, we find that the spatial scale and advection can affect Hopf bifurcation in the heterogenous environment.
中文翻译:
异质环境中时滞扩散物流种群模型的分叉分析。
在本文中,我们研究了一个延迟的反应扩散对流方程,该方程对流非均质环境中的种群动态进行建模。获得了非恒定正稳态和相关的Hopf分叉的存在。引入与对流速率相关的加权内积来计算正态形式,这是延迟反应-扩散-对流模型与延迟反应-扩散模型的Hopf分叉的主要区别。此外,我们发现空间尺度和对流会影响异质环境中的Hopf分叉。
更新日期:2019-03-08
中文翻译:
异质环境中时滞扩散物流种群模型的分叉分析。
在本文中,我们研究了一个延迟的反应扩散对流方程,该方程对流非均质环境中的种群动态进行建模。获得了非恒定正稳态和相关的Hopf分叉的存在。引入与对流速率相关的加权内积来计算正态形式,这是延迟反应-扩散-对流模型与延迟反应-扩散模型的Hopf分叉的主要区别。此外,我们发现空间尺度和对流会影响异质环境中的Hopf分叉。