Abstract We study two mathematical models consisting of nonlinear systems of partial differential equations, a predator prey and a competitive two-species chemotaxis systems with two chemicals satisfying their corresponding elliptic equations in a smooth bounded domain. By introducing global factors, for different ranges of parameters and by deriving a discretization of the system by means of the Generalized Finite Difference Method (GFDM) we prove that any positive and bounded discrete solution converges to the analytical one, i.e., a spatially homogeneous state. We apply the meshless method over regular and irregular domains where we simulate the behavior of the solution with the tools of several numerical examples.

中文翻译：

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通过无网格方法对猎物-捕食者相互作用进行收敛和数值模拟

摘要 我们研究了由偏微分方程非线性系统、捕食者猎物和竞争性二物种趋化系统组成的两个数学模型，其中两种化学物质在光滑有界域中满足其相应的椭圆方程。通过引入全局因子，对于不同范围的参数，并通过广义有限差分法 (GFDM) 推导出系统的离散化，我们证明任何正的和有界的离散解收敛到解析解，即空间齐次状态. 我们在规则和不规则域上应用无网格方法，在这些域中我们使用几个数值示例的工具来模拟解的行为。