A reaction–diffusion system is formulated to describe three interacting species within the Hastings–Powell (HP) food chain structure with chemotaxis produced by three chemicals. We construct a finite volume (FV) scheme for this system, and in combination with the non-negativity and a priori estimates for the discrete solution, the existence of a discrete solution of the FV scheme is proven. It is shown that the scheme converges to the corresponding weak solution of the model. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space–time $L^1$ compactness argument. Finally, numerical tests illustrate the model and the behavior of the FV scheme.

建立了反应扩散系统，以描述黑斯廷斯-鲍威尔（HP）食物链结构中的三种相互作用的物种，其中三种化学物质产生趋化性。我们为此系统构造了一个有限体积（FV）方案，并结合离散化解的非负性和先验估计，证明了FV方案离散解的存在。结果表明，该方案收敛到模型的相应弱解。收敛证明在各种应用中使用了两个重要的因素，即具有一般边界条件和时空的离散Sobolev嵌入不等式${\mathrm{大号}}^{\mathrm{1个}}$紧凑性参数。最后，数值测试说明了FV方案的模型和行为。