洛特卡-伏特拉混合系统解的终极边界性和永久性条件

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-09-05 DOI:10.3103/s1066369x24700440

A. V. Platonov

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引用次数: 0

摘要

摘要本文考虑了一个带开关的广义 Lotka-Volterra 型系统。研究了解的最终有界性和系统持久性的条件。借助直接李雅普诺夫方法，建立了对切换规律的要求，以保证系统的必要动态性。在系统的相空间中构建了一个有吸引力的紧凑不变集，并为这个集提供了一个给定的吸引力区域。这项工作的一个显著特点是使用了两种不同的 Lyapunov 函数组合，每种函数在解决问题时都发挥着各自的特殊作用。

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Conditions for Ultimate Boundedness of Solutions and Permanence for a Hybrid Lotka–Volterra System

Abstract

In the paper, a generalized Lotka–Volterra-type system with switching is considered. The conditions for the ultimate boundedness of solutions and the permanence of the system are studied. With the aid of the direct Lyapunov method, the requirements for the switching law are established to guarantee the necessary dynamics of the system. An attractive compact invariant set is constructed in the phase space of the system, and a given region of attraction for this set is provided. A distinctive feature of the work is the use of a combination of two different Lyapunov functions, each of which plays its own special role in solving the problem.

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来源期刊

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.