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Abstract <p> The conditions linking the strict selection property in continuous- and discrete-timedynamical systems on a standard simplex are investigated. These conditions permit choosing theintegration step adequately without losing the strict selection property in the system. An attemptis made to link the concepts of selection for difference systems with the corresponding differentialanalog. It is shown that if the solution of a difference system uniformly converges to the vertex ofthe simplex, then the original differential systems possess the selection property as well and arewidely used in constructing mathematical models of various real-world processes.</p>

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Relation Between Selection Concepts for Systems of Differential and Difference Equations on a Standard Finite-Dimensional Simplex

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • D. V. Kapitanov,
  • O. A. Kuzenkov,
  • V. V. Fomichev

摘要

Abstract

The conditions linking the strict selection property in continuous- and discrete-timedynamical systems on a standard simplex are investigated. These conditions permit choosing theintegration step adequately without losing the strict selection property in the system. An attemptis made to link the concepts of selection for difference systems with the corresponding differentialanalog. It is shown that if the solution of a difference system uniformly converges to the vertex ofthe simplex, then the original differential systems possess the selection property as well and arewidely used in constructing mathematical models of various real-world processes.