Scholarlink

<p>We study the classical chemostat model when lateral gene transfer is taken into account and the removal rates of the strains are distinct. We extend some results from the existing literature, obtained in the case of two strains and also in the general case of <b>n</b> strains, when the removal rates are equal to the dilution rate of the chemostat. We demonstrate the existence and uniqueness of the coexistence equilibrium at which all strains coexist, provided that the chemostat input concentration exceeds a critical value, that can be calculated explicitly. We demonstrate that when the different genotypes have equal growth rate functions, the coexistence equilibrium is globally asymptotically stable. When all yields are equal and the removal rates are equal to the dilution rate, the system satisfies the conservation principle and can be reduced to an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varvec{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold-italic">n</mi> </mrow> </math></EquationSource> </InlineEquation>-dimensional system, where <i>n</i> is the number of strains. We show that for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n=3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>, the positive equilibrium can be unstable, with the appearance of Hopf bifurcations and limit cycles. Such behavior does not occur in the case of two strains.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The Chemostat with Lateral Gene Transfer and Distinct Removal Rates

  • 期刊论文

  • 发表日期：

    2026年6月30日

查看全文
  • Tewfik Sari

摘要

We study the classical chemostat model when lateral gene transfer is taken into account and the removal rates of the strains are distinct. We extend some results from the existing literature, obtained in the case of two strains and also in the general case of n strains, when the removal rates are equal to the dilution rate of the chemostat. We demonstrate the existence and uniqueness of the coexistence equilibrium at which all strains coexist, provided that the chemostat input concentration exceeds a critical value, that can be calculated explicitly. We demonstrate that when the different genotypes have equal growth rate functions, the coexistence equilibrium is globally asymptotically stable. When all yields are equal and the removal rates are equal to the dilution rate, the system satisfies the conservation principle and can be reduced to an \(\varvec{n}\) n -dimensional system, where n is the number of strains. We show that for \(n=3\) n = 3 , the positive equilibrium can be unstable, with the appearance of Hopf bifurcations and limit cycles. Such behavior does not occur in the case of two strains.