具有避难状态的混合种群动力学模型：正则化和极限集

IF 0.58 Q3 Engineering

Journal of Applied and Industrial Mathematics Pub Date : 2025-07-11 DOI:10.1134/S1990478924040082

A. N. Kirillov, A. M. Sazonov

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引用次数: 0

摘要

本文研究了种群“捕食者-猎物”动态与猎物种内竞争的正则化问题。该模型具有两个二维系统相互切换的混合系统的形式。系统的切换使我们能够在猎物数量很少、捕食者很难找到猎物的情况下重现特殊的避难所制度。给出了利用双开关线对系统进行正则化以避免抖振的方法。建立了正则化模型的极限集。研究了模型对开关的灵敏度。推导了杂化不改变平衡整体稳定性的条件。在另一种情况下，极限集是环。

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A Model of Hybrid Population Dynamics with Refuge-Regime: Regularization and Limit Sets

The paper is devoted to the regularization of the population “predator-prey” dynamics with the preys’ intraspecific competition. The model has the form of the hybrid system consisting of the two two-dimensional systems switching between each other. The switching of the systems allows us to reproduce the special Refuge-regime when the prey number is very small and the predators have complications to find preys. The regularization of the system by using two switching lines to avoid chattering is provided. The limit sets for the regularized model are established. The model sensitivity to the switchings is investgated. The condition under which the hybridization does not change the global stability of an equilibrium is derived. In the other case the limit sets are cycles.

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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.