AI 中文总结
本文研究带非常数扩散的Lotka-Volterra反应-扩散系统，构造多参数精确解，证明其满足零Neumann条件及存在两个稳定稳态点，用精确解求解边值问题并验证小扰动下数值解与精确解吻合度高。
AI 中文摘要
本文研究一类具有多孔扩散的Lotka-Volterra型系统，该系统可作为经典Lotka-Volterra系统的替代模型。文中构造了该系统的多参数族精确解并确立其性质，证明所得解可满足零Neumann条件（描述实际过程的数学模型的典型条件）。还证明当系数选取恰当时，该系统存在两个稳定稳态点，尤其在模拟捕食者-猎物相互作用时成立。将精确解用于求解边值问题，分析结果与相同边值问题的数值解（初始剖面受扰动）对比，结果表明当初始剖面扰动足够小时，数值解与对应精确解的吻合度极高。
英文摘要
A Lotka-Volterra type system with porous diffusion, which can be used as an alternative model to the classical Lotka-Volterra system, is under study. Multiparameter families of exact solutions of the system in question are constructed and their properties are established. It is shown that the solutions obtained can satisfy the zero Neumann conditions, which are typical conditions for mathematical models describing real-world processes. It is proved that the system possesses two stable steady-state points provided its coefficients are correctly-specified. In particular, this occurs when the system models the prey-predator interaction. The exact solutions are used for solving boundary-value problems. The analytical results are compared with numerical solutions of the same boundary-value problems but perturbed initial profiles. It is demonstrated that the numerical solutions coincide with the relevant exact solutions with high exactness in the case of sufficiently small perturbations of the initial profiles.
Comments21 pages, 7 figures
Journal refAxioms, 2025, vol.14, 655
