Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Multiple limit cycles in the chemostat with variable yield.

Sergei S Pilyugin1, Paul Waltman

  • 1Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA. pilyugin@math.ufl.edu

Mathematical Biosciences
|February 20, 2003
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Effect of transcriptional delay on ribosome abundance control.

Journal of mathematical biology·2026
Same author

Revealing hidden drivers of Lassa fever through a model-informed approach for reproducing and predicting disease dynamics and guiding control strategies.

Scientific reports·2025
Same author

Mobility and its sensitivity to fitness differences determine consumer-resource distributions.

Royal Society open science·2020
Same author

Habitat-dependent movement rate can determine the efficacy of marine protected areas.

Ecology·2018
Same author

The effectiveness of marine protected areas for predator and prey with varying mobility.

Theoretical population biology·2016
Same author

Trans-membrane area asymmetry controls the shape of cellular organelles.

International journal of molecular sciences·2015

The variable yield model, unlike the Monod model, shows sustained oscillations and multiple limit cycles. This mathematical model has implications for understanding how competing populations coexist in ecosystems.

Area of Science:

  • Mathematical Biology
  • Ecology
  • Dynamical Systems

Background:

  • The Monod model is a cornerstone in microbial ecology, describing substrate-limited growth.
  • Previous models often assume a constant yield coefficient, simplifying ecological dynamics.
  • Understanding population dynamics requires accurate modeling of microbial growth and nutrient interactions.

Purpose of the Study:

  • To analyze the global asymptotic behavior of solutions for the variable yield model.
  • To generalize the classical Monod model by incorporating a yield that varies with nutrient concentration.
  • To investigate the emergence of complex dynamics, such as oscillations and multiple stable states.

Main Methods:

  • Asymptotic analysis of differential equations governing the variable yield model.

Related Experiment Videos

  • Bifurcation analysis to identify critical transitions in model behavior.
  • Qualitative analysis of solution trajectories in phase space.

    • Main Results:

    • The variable yield model demonstrates sustained oscillations, a behavior absent in the standard Monod model.
    • A subcritical Hopf bifurcation is identified, indicating a sudden change in system stability.
    • The model can exhibit at least two distinct limit cycles, suggesting multiple possible stable states for populations.

    Conclusions:

    • The variable yield model offers a more nuanced representation of microbial growth dynamics.
    • The presence of oscillations and multiple limit cycles has significant implications for species coexistence and ecosystem stability.
    • This generalized model provides new insights into the complex interactions within microbial communities.