Numerical proof for chemostat chaos of Shilnikov's type

Bo Deng, Maoan Han, Sze Bi Hsu

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A classical chemostat model is considered that models the cycling of one essential abiotic element or nutrient through a food chain of three trophic levels. The long-time behavior of the model was known to exhibit complex dynamics more than 20 years ago. It is still an open problem to prove the existence of chaos analytically. In this paper, we aim to solve the problem numerically. In our approach, we introduce an artificial singular parameter to the model and construct singular homoclinic orbits of the saddle-focus type which is known for chaos generation. From the configuration of the nullclines of the equations that generates the singular homoclinic orbits, a shooting algorithm is devised to find such Shilnikov saddle-focus homoclinic orbits numerically which in turn imply the existence of chaotic dynamics for the original chemostat model.

Original languageEnglish (US)
Article number033106
JournalChaos
Volume27
Issue number3
DOIs
StatePublished - Mar 1 2017

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Chemostats
Chemostat
Homoclinic Orbit
Chaos theory
Chemostat Model
chaos
Chaos
Saddle
Orbits
saddles
Food Chain
orbits
Shooting
Cycling
Chaotic Dynamics
Long-time Behavior
Complex Dynamics
Nutrients
food chain
Open Problems

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Numerical proof for chemostat chaos of Shilnikov's type. / Deng, Bo; Han, Maoan; Hsu, Sze Bi.

In: Chaos, Vol. 27, No. 3, 033106, 01.03.2017.

Research output: Contribution to journalArticle

Deng, Bo ; Han, Maoan ; Hsu, Sze Bi. / Numerical proof for chemostat chaos of Shilnikov's type. In: Chaos. 2017 ; Vol. 27, No. 3.
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