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 Concept Videos

Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

1.3K
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
1.3K
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

1.3K
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
1.3K
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

438
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
438
Slant Asymptotes01:27

Slant Asymptotes

264
A function's behavior is often guided by asymptotic constraints, where one term dominates another, defining a limiting trend. In the given scenario, the mathematical pattern follows a rational function: a cubic term in the numerator is divided by a squared term in the denominator. This results in a function with distinct characteristics, including an oblique asymptote, critical points, and undefined regions.The function's validity is determined by the denominator, which must be nonzero. This...
264
Typical Model Studies01:30

Typical Model Studies

842
Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
842
Continuity of a Function01:23

Continuity of a Function

404
A function is continuous at a point a if three conditions are met: the function is defined at a, the limit of the function as x approaches a exists, and this limit equals the function’s value. Mathematically, this is written asThis definition ensures the graph of the function does not exhibit any breaks, holes, or jumps at that point. Discontinuities occur when any of these conditions fail. A removable discontinuity exists when the two-sided limit exists but the function is either...
404

You might also read

Related Articles

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

Sort by
Same author

Revealing new dynamical patterns in a reaction-diffusion model with cyclic competition via a novel computational framework.

Proceedings. Mathematical, physical, and engineering sciences·2018
Same author

Quantifying uncertainty in partially specified biological models: how can optimal control theory help us?

Proceedings. Mathematical, physical, and engineering sciences·2016
Same author

Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect.

Journal of theoretical biology·2016
Same author

Revisiting the Stability of Spatially Heterogeneous Predator-Prey Systems Under Eutrophication.

Bulletin of mathematical biology·2015
Same author

Defining and detecting structural sensitivity in biological models: developing a new framework.

Journal of mathematical biology·2014
Same author

Revising the role of species mobility in maintaining biodiversity in communities with cyclic competition.

Bulletin of mathematical biology·2012

Related Experiment Video

Updated: Apr 30, 2026

Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation
11:41

Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation

Published on: February 1, 2020

18.1K

Bifurcation analysis of models with uncertain function specification: how should we proceed?

M W Adamson1, A Yu Morozov

  • 1Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK.

Bulletin of Mathematical Biology
|May 3, 2014
PubMed
Summary

This study introduces a new framework for analyzing biological models with uncertain functions, moving beyond fixed mathematical forms. It proposes a probabilistic approach to understand bifurcations, crucial for predicting model dynamics.

Related Experiment Videos

Last Updated: Apr 30, 2026

Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation
11:41

Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation

Published on: February 1, 2020

18.1K

Area of Science:

  • Mathematical Biology
  • Dynamical Systems Theory
  • Theoretical Ecology

Background:

  • Traditional models assume precisely defined functions, leading to clear bifurcation structures.
  • Biological models often involve functions with unknown exact forms, only specified by qualitative properties.
  • Existing methods to handle function uncertainty impose restrictive, biologically irrelevant constraints.

Purpose of the Study:

  • To develop a novel framework for analyzing deterministic biological models with unspecified functions.
  • To address the ambiguity arising from unknown function shapes in dynamical systems.
  • To propose a probabilistic method for characterizing bifurcations under parameter uncertainty.

Main Methods:

  • Utilizing the Ordinary Differential Equation (ODE) paradigm.
  • Developing a framework to analyze models where function formulations are not fully specified.
  • Introducing a method to calculate the probability of bifurcation events.
  • Illustrating with a predator-prey model featuring logistic-type prey growth uncertainty.

Main Results:

  • The conventional concept of a concrete bifurcation structure is shown to be irrelevant for models with unspecified functions.
  • Bifurcations in such models can only be described probabilistically.
  • A method for quantifying bifurcation probability under parameter uncertainty is presented.
  • The study demonstrates evaluating the probability of supercritical versus subcritical Hopf bifurcations in a predator-prey model.

Conclusions:

  • A probabilistic framework is essential for understanding bifurcations in biological models with uncertain functions.
  • The proposed method allows for more realistic analysis of dynamical systems where function forms are not precisely known.
  • This approach enhances the biological relevance and interpretability of model predictions.