A nonlocal swarm model for predators-prey interactions
A nonlocal swarm model for predators-prey interactions
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DOI：
10.1142/s0218202516400042
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发表时间：
2016-02-01
影响因子：
3.5
通讯作者：
Fagioli, Simone
中科院分区：
文献类型：
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作者：
Di Francesco, Marco;Fagioli, Simone
我们考虑了两个物种的非局部相互作用偏微分方程模型的捕食者和猎物的群集动力学，其中所有的代理通过梯度型的吸引力/排斥力相互作用。为了模拟捕食者-猎物相互作用，我们规定比例势（符号相反）的交叉相互作用的一部分。该模型有一个基于粒子的离散（ODE）版本和连续PDE版本。我们以系统的形式研究了常微分方程组中粒子定态解的结构及其稳定性，并给出了简单的例子。然后，我们证明了稳定的粒子定常状态是局部稳定的完全非线性连续模型，提供了一个轻微的加强粒子的条件是必需的。后一个结果在一维空间中成立。我们用简单的数值模拟补充了所有的粒子例子，并提供了一些二维例子来突出系统在大时间行为中的复杂性。
We consider a two-species system of nonlocal interaction PDEs modeling the swarming dynamics of predators and prey, in which all agents interact through attractive/repulsive forces of gradient type. In order to model the predator-prey interaction, we prescribed proportional potentials (with opposite signs) for the cross-interaction part. The model has a particle-based discrete (ODE) version and a continuum PDE version. We investigate the structure of particle stationary solution and their stability in the ODE system in a systematic form, and then consider simple examples. We then prove that the stable particle steady states are locally stable for the fully nonlinear continuum model, provided a slight reinforcement of the particle condition is required. The latter result holds in one space dimension. We complement all the particle examples with simple numerical simulations, and we provide some two-dimensional examples to highlight the complexity in the large time behavior of the system.