The paper is concerned with a nonlinear system of delayed differential equations as a generalization of an equation describing a simple model of the fluctuation of biological populations. The dependence of the behavior of monotone solutions on the coefficients and delays is studied and optimal sufficient conditions are derived for the existence of increasing and unbounded solutions and for the existence of increasing and convergent solutions. Inequalities estimating such solutions with some given increasing functions are derived as well. The results are compared with the linear case illustrated by examples, and open problems are formulated.

中文翻译：

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非线性时滞微分方程的收敛解和渐进解。

本文关注的是非线性时滞微分方程组，作为描述生物种群波动简单模型的方程组的推广。研究了单调解的行为对系数和时滞的依赖性，并为增长解和无界解的存在以及增长解和收敛解的存在导出了最佳的充分条件。还推导了使用某些给定的递增函数来估计此类解的不等式。将结果与示例所示的线性情况进行比较，并提出未解决的问题。