An exact bifurcation diagram for a reaction–diffusion equation arising in population dynamics
An exact bifurcation diagram for a reaction–diffusion equation arising in population dynamics
复制标题
群体动力学中出现的反应扩散方程的精确分岔图
DOI：
10.1186/s13661-018-1090-z
复制
发表时间：
2018
影响因子：
1.7
通讯作者：
R. Shivaji
中科院分区：
文献类型：
--
作者：
Jerome Goddard Ii;Q. Morris;S. Robinson;R. Shivaji
摘要我们分析了以下问题的正解：
{−Δv=λv(1−v)；Ω0，∂v∂η+γλv=0；∂Ω0，$$\TextStyle\Begin{Case}-\Delta v=\lambda v(1-v)；&\\Frc{\Partial v}{\Partial\Eta}+\Gamma\Sqrt{\lambda}v=0；&\Partial\Omega_{0}，\end{Case}$$其中Ω0=(0，1)$\Omega_{0}=(0，1)$或者是Rn$\Mathbb{R}^{n}$中的有界域，n=2，3$n=2，3$，边界光滑，|Ω0|=1$|\omega_{0}|=1$，λ，γ为正参数。这样的稳态方程出现在种群动力学中，其中封装了关于斑块/矩阵界面的假设，如斑块偏好和运动行为。在本文中，我们将讨论这类稳态模型的精确分岔图和稳定性性质。
AbstractWe analyze the positive solutions to
{−Δv=λv(1−v);Ω0,∂v∂η+γλv=0;∂Ω0,$$ \textstyle\begin{cases} - \Delta v = \lambda v(1-v); & \Omega_{0}, \\ \frac{\partial v}{\partial\eta} + \gamma\sqrt{\lambda} v =0 ; & \partial\Omega_{0}, \end{cases} $$ where Ω0=(0,1)$\Omega_{0}=(0,1)$ or is a bounded domain in Rn$\mathbb{R}^{n}$, n=2,3$n =2,3$, with smooth boundary and |Ω0|=1$|\Omega_{0}|=1$, and λ, γ are positive parameters. Such steady state equations arise in population dynamics encapsulating assumptions regarding the patch/matrix interfaces such as patch preference and movement behavior. In this paper, we will discuss the exact bifurcation diagram and stability properties for such a steady state model.