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Abstract <p> We study stability conditions for the trivial equilibrium of a linear nonautonomousdifferential equation with variable delay arising in simulation of population dynamics. Thisequation is supplemented by an auxiliary equation reflecting dynamics of the number ofindividuals in the population at an intermediate stage of development. We analyze stability ofthe trivial equilibrium of the basic equation with the use of Lyapunov–Krasovskiĭfunctionals and the method of integral inequalities. We construct upper and lower exponentialestimates of solutions of the Cauchy problems for the basic and auxiliary equations.</p>

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Stability and Two-Sided Estimates of Solutions of a Linear Nonautonomous Differential Equation with Variable Delay

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • N. V. Pertsev

摘要

Abstract

We study stability conditions for the trivial equilibrium of a linear nonautonomousdifferential equation with variable delay arising in simulation of population dynamics. Thisequation is supplemented by an auxiliary equation reflecting dynamics of the number ofindividuals in the population at an intermediate stage of development. We analyze stability ofthe trivial equilibrium of the basic equation with the use of Lyapunov–Krasovskiĭfunctionals and the method of integral inequalities. We construct upper and lower exponentialestimates of solutions of the Cauchy problems for the basic and auxiliary equations.