SIAM Journal on Applied Mathematics, Volume 81, Issue 2, Page 407-433, January 2021.
It is well known that movement strategies in ecology and in economics can make the difference between extinction and persistence. We present a unifying model for the dynamics of ecological populations and street vendors, which are an important part of many informal economies. We analyze this model to study the effects of directed movement of populations subject to strong Allee effect. We begin with the study of the existence of equilibrium solutions subject to homogeneous Dirichlet or no-flux boundary conditions. Next, we study the evolution problem and show that if the directed movement effect is small, the solutions behave like those of the classical reaction-diffusion equation with bistable growth pattern. We present numerical simulations, which show that directed movement can help overcome a strong Allee effect and provide some partial analytical results in this direction. We conclude by making a connection to the ideal free distribution and analyze what happens under competition, finding that an ideal free distribution strategy is a local neighborhood invader.

中文翻译：

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定向运动对强Allee效应的影响

SIAM应用数学杂志，第81卷，第2期，第407-433页，2021年1月。
众所周知，生态和经济学中的运动策略可以使灭绝和持久性有所不同。我们提出了生态人口和街头小贩动态的统一模型，这是许多非正规经济的重要组成部分。我们分析此模型以研究受强Allee效应影响的人口定向运动的影响。我们从研究均质Dirichlet或无通量边界条件的平衡解的存在开始。接下来，我们研究了演化问题，并表明，如果定向运动效应较小，则解的行为类似于具有双稳态增长模式的经典反应扩散方程。我们提出数值模拟，这表明定向运动可以帮助克服强烈的Allee效应，并在此方向上提供一些部分分析结果。我们通过与理想的自由分配建立联系并分析竞争中发生的情况，得出结论，理想的自由分配策略是本地邻居入侵者。