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

Predator-Prey Interactions02:39

Predator-Prey Interactions

22.4K
Predators consume prey for energy. Predators that acquire prey and prey that avoid predation both increase their chances of survival and reproduction (i.e., fitness). Routine predator-prey interactions elicit mutual adaptations that improve predator offenses, such as claws, teeth, and speed, as well as prey defenses, including crypsis, aposematism, and mimicry. Thus, predator-prey interactions resemble an evolutionary arms race.
22.4K
Optimal Foraging00:48

Optimal Foraging

14.4K
How animals obtain and eat their food is called foraging behavior. Foraging can include searching for plants and hunting for prey and depends on the species and environment.
14.4K
Modeling with Differential Equations01:25

Modeling with Differential Equations

289
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
289
What are Populations and Communities?00:30

What are Populations and Communities?

38.9K
Overview
38.9K
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

415
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...
415
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

431
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
431

You might also read

Related Articles

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

Sort by
Same author

On quasi-linear reaction diffusion systems arising from compartmental SEIR models.

Nonlinear differential equations and applications : NoDEA·2024
Same author

Smartphone use for Paediatric Calculations in Emergencies (SPaCE).

Archives of disease in childhood·2023
Same author

Review of the 2021 Resuscitation Council United Kingdom guideline for the emergency treatment of anaphylaxis.

Archives of disease in childhood. Education and practice edition·2022
Same author

Fifteen-minute consultation: Recognition of sickle cell crises in the paediatric emergency department.

Archives of disease in childhood. Education and practice edition·2021
Same author

Fifteen-minute consultation: Drowning in children.

Archives of disease in childhood. Education and practice edition·2020
Same author

Fifteen-minute consultation: How to be the paediatrician at a trauma call.

Archives of disease in childhood. Education and practice edition·2019

Related Experiment Video

Updated: Apr 18, 2026

A Real-Time Interactive System for Studying Confrontational Pursuit Behavior in Rodents
06:25

A Real-Time Interactive System for Studying Confrontational Pursuit Behavior in Rodents

Published on: May 16, 2025

1.7K

Simple finite element methods for approximating predator-prey dynamics in two dimensions using MATLAB.

Marcus R Garvie1, John Burkardt, Jeff Morgan

  • 1Department of Mathematics and Statistics, University of Guelph, Guelph, ON, N1G 2W1, Canada, mgarvie@uoguelph.ca.

Bulletin of Mathematical Biology
|January 25, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces finite element methods to model predator-prey dynamics, offering new insights into how habitat shape and boundary conditions influence these ecological interactions.

More Related Videos

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

706
Methodology for Developing Life Tables for Sessile Insects in the Field Using the Whitefly, Bemisia tabaci, in Cotton As a Model System
09:23

Methodology for Developing Life Tables for Sessile Insects in the Field Using the Whitefly, Bemisia tabaci, in Cotton As a Model System

Published on: November 1, 2017

12.7K

Related Experiment Videos

Last Updated: Apr 18, 2026

A Real-Time Interactive System for Studying Confrontational Pursuit Behavior in Rodents
06:25

A Real-Time Interactive System for Studying Confrontational Pursuit Behavior in Rodents

Published on: May 16, 2025

1.7K
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

706
Methodology for Developing Life Tables for Sessile Insects in the Field Using the Whitefly, Bemisia tabaci, in Cotton As a Model System
09:23

Methodology for Developing Life Tables for Sessile Insects in the Field Using the Whitefly, Bemisia tabaci, in Cotton As a Model System

Published on: November 1, 2017

12.7K

Area of Science:

  • Mathematical Biology
  • Computational Ecology
  • Numerical Analysis

Background:

  • Predator-prey dynamics are fundamental to ecosystem stability.
  • Previous models often used simplified domains and boundary conditions.
  • The Holling type II functional response and logistic prey growth are key ecological factors.

Purpose of the Study:

  • To develop and present simple finite element schemes for spatially extended predator-prey models.
  • To provide open-source MATLAB code for implementing these methods.
  • To investigate the influence of domain shape and boundary conditions on ecological dynamics.

Main Methods:

  • Finite element schemes for predator-prey models with Holling type II response.
  • Generalization of existing numerical schemes.
  • Implementation on arbitrary 2D domains with various boundary conditions (Dirichlet, Neumann, Robin, Periodic).

Main Results:

  • Demonstration of the crucial role of habitat shape, initial data, and boundary conditions.
  • Numerical experiments reveal complex spatiotemporal dynamics.
  • The developed methods are applicable to diverse ecological scenarios.

Conclusions:

  • The study provides a flexible numerical framework for ecological modeling.
  • Habitat geometry and boundary conditions significantly impact predator-prey interactions.
  • This work advances the understanding of spatially explicit ecological dynamics.