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<p>In this paper, we focus on investigating a novel kind of cycled system that models the cell growth and division process. The research is mainly conducted in two aspects. Firstly, for the linear problem, we construct a Cauchy matrix to present its solution and study the properties of the Cauchy matrix. By using these properties, we propose different sufficient conditions to ensure the finite time stability. Secondly, regarding the nonlinear problem, based on the establishment of the existence and uniqueness of its solution, we investigate its finite time stability. Finally, examples are used to verify our results. These theoretical results are valuable for the study of cell growth and division, as well as the cycled phenomena in biology, physiology and other related fields.</p>

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Finite time stability analysis for a new type of cycled system

  • 期刊论文

  • 发表日期：

    2025年2月12日

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  • Yuanlin Ding,
  • Rui Liu

摘要

In this paper, we focus on investigating a novel kind of cycled system that models the cell growth and division process. The research is mainly conducted in two aspects. Firstly, for the linear problem, we construct a Cauchy matrix to present its solution and study the properties of the Cauchy matrix. By using these properties, we propose different sufficient conditions to ensure the finite time stability. Secondly, regarding the nonlinear problem, based on the establishment of the existence and uniqueness of its solution, we investigate its finite time stability. Finally, examples are used to verify our results. These theoretical results are valuable for the study of cell growth and division, as well as the cycled phenomena in biology, physiology and other related fields.