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Periodic solutions for a delayed competitive chemostat model with periodic nutrient input and rate

Teresa Faria

TL;DR

A nonautonomous periodic chemostat model with delays modelling n species in competition is considered, and sufficient conditions on the coefficients and consumption functions for the species are given to ensure the existence of n nontrivial and nonnegative periodic solutions.

Abstract

A nonautonomous periodic chemostat model with delays modelling $n$ species in competition is considered. Sufficient conditions on the coefficients and consumption functions for the species are given, for both the extinction of the species and for the existence of $n$ nontrivial and nonnegative periodic solutions. Further criteria guarantee that the system admits at least one strictly positive periodic solution.

Periodic solutions for a delayed competitive chemostat model with periodic nutrient input and rate

TL;DR

A nonautonomous periodic chemostat model with delays modelling n species in competition is considered, and sufficient conditions on the coefficients and consumption functions for the species are given to ensure the existence of n nontrivial and nonnegative periodic solutions.

Abstract

A nonautonomous periodic chemostat model with delays modelling species in competition is considered. Sufficient conditions on the coefficients and consumption functions for the species are given, for both the extinction of the species and for the existence of nontrivial and nonnegative periodic solutions. Further criteria guarantee that the system admits at least one strictly positive periodic solution.
Paper Structure (5 sections, 15 theorems, 83 equations)

This paper contains 5 sections, 15 theorems, 83 equations.

Table of Contents

  1. Introduction
  2. Preliminary results and extinction
  3. Existence of nontrivial periodic solutions
  4. Competitive exclusion, coexistence, attractivity
  5. Conclusions and discussion

Key Result

Lemma 2.1

Assume (H1)-(H2). For a nonnegative solution $(S(t),x_1(t),\dots,x_n(t))$ of Chem, define Then $y(t)$ is a positive solution of the ODE and satisfies

Theorems & Definitions (33)

  • Lemma 2.1
  • Remark 2.1
  • Lemma 2.2
  • Theorem 2.1
  • proof
  • Remark 2.2
  • Remark 2.3
  • Lemma 3.1
  • proof
  • Theorem 3.1
  • ...and 23 more