Abstract

A nonlinear integral equation arising from a parametric closure of the third spatial moment in the single-species model of logistic dynamics of U. Dieckmann and R. Law is analyzed. The case of piecewise constant kernels is studied, which is important for further computer modeling. Sufficient conditions are found that guarantee the existence of a nontrivial solution to the equilibrium equation. The use of constant kernels makes it possible to obtain more accurate results compared to earlier works, in particular, more accurate estimates for the L₁ norm of the solution and for the closure parameter are obtained.

中文翻译：

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分段常核情况下Logistic动力学模型非线性积分方程组的可解性分析

摘要

分析了 U. Dieckmann 和 R. Law 的逻辑动力学单物种模型中第三空间矩的参数闭包所产生的非线性积分方程。研究了分段常数核的情况，这对于进一步的计算机建模很重要。找到了保证平衡方程非平凡解存在的充分条件。与早期的工作相比，使用恒定内核可以获得更准确的结果，特别是获得对解的L ₁范数和闭包参数的更准确的估计。