A Multispecies Cross-Diffusion Model for Territorial Development
A Multispecies Cross-Diffusion Model for Territorial Development
复制标题
领土发展的多物种交叉扩散模型
作者：
Abdulaziz Alsenafi;Alethea B. T. Barbaro
我们在格子上开发了一个基于主体的模型来研究由涂鸦等标记引起的领土发展，推广了先前发表的模型，以解释K组而不是两个组。然后，我们分析了这个模型，并提出了两个新的变化。我们的模型假设代理人的运动是一种偏离对手群体标记的有偏见的随机行走。所有代理之间的相互作用都是间接的，通过标记进行调解。我们用数值方法证明了在三群系统中，群在一定的参数范围内是分离的。从离散模型出发，正式导出了该模型的2K对流扩散方程的连续统。由于避免了对手群的标记，这些方程表现出交叉扩散。通过数值模拟和连续统系统的线性稳定性分析，我们发现k群模型与两群模型具有许多相同的性质。然后，我们引入了基于智能体模型的两种新变体，一种对应于一些群体比其他群体更胆小，另一种对应于一些群体比其他群体更具威胁性。这些变化呈现出与原始模型中发现的不同的领土模式。我们推导了这些变化的对流扩散方程的相应系统，通过数值和线性稳定性分析发现每个变化都表现出相变。
We develop an agent-based model on a lattice to investigate territorial development motivated by markings such as graffiti, generalizing a previously-published model to account for K groups instead of two groups. We then analyze this model and present two novel variations. Our model assumes that agents’ movement is a biased random walk away from rival groups’ markings. All interactions between agents are indirect, mediated through the markings. We numerically demonstrate that in a system of three groups, the groups segregate in certain parameter regimes. Starting from the discrete model, we formally derive the continuum system of 2K convection–diffusion equations for our model. These equations exhibit cross-diffusion due to the avoidance of the rival groups’ markings. Both through numerical simulations and through a linear stability analysis of the continuum system, we find that many of the same properties hold for the K-group model as for the two-group model. We then introduce two novel variations of the agent-based model, one corresponding to some groups being more timid than others, and the other corresponding to some groups being more threatening than others. These variations present different territorial patterns than those found in the original model. We derive corresponding systems of convection–diffusion equations for each of these variations, finding both numerically and through linear stability analysis that each variation exhibits a phase transition.
影响因子：
1.9
作者：
Chuntian Wang;Y. Zhang;A. Bertozzi;M. Short
通讯作者：
Chuntian Wang;Y. Zhang;A. Bertozzi;M. Short