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

Forest defoliation scenarios.

Glenn Ledder1

  • 1Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0130, USA. gledder@math.unl.edu

Mathematical Biosciences and Engineering : MBE
|July 31, 2007
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

Optimal allocation of two resources in annual plants.

Mathematical biosciences and engineering : MBE·2025
Same author

Incorporating changeable attitudes toward vaccination into compartment models for infectious diseases.

Mathematical biosciences and engineering : MBE·2025
Same author

Using asymptotics for efficient stability determination in epidemiological models.

Mathematical biosciences and engineering : MBE·2025
Same author

Dynamic Energy Budget models: fertile ground for understanding resource allocation in plants in a changing world.

Conservation physiology·2022
Same author

Incorporating mass vaccination into compartment models for infectious diseases.

Mathematical biosciences and engineering : MBE·2022
Same author

Mentoring Undergraduate Research in Mathematical Modeling.

Bulletin of mathematical biology·2022
Same journal

Modeling the impact of budget limitation on the screening and treatment pathway of HPV-induced precancerous cervical lesions.

Mathematical biosciences and engineering : MBE·2026
Same journal

Modeling the effects of trait-mediated dispersal on coexistence of two species: Competition and non-consumptive predator-prey.

Mathematical biosciences and engineering : MBE·2026
Same journal

A close look at the viral reduction rate in target cell limited models.

Mathematical biosciences and engineering : MBE·2026
Same journal

A stochastic agent-based model for simulating tumor-immune dynamics and evaluating therapeutic strategies.

Mathematical biosciences and engineering : MBE·2026
Same journal

Addressing domain shift via imbalance-aware domain adaptation in embryo development assessment.

Mathematical biosciences and engineering : MBE·2026
Same journal

Effect of drug resistance on an HIV epidemic in heterogeneous populations.

Mathematical biosciences and engineering : MBE·2026
See all related articles

This study analyzes a mathematical model of spruce budworm infestations, revealing how different time scales and population mechanisms create complex forest dynamics. Understanding these dynamics is key to predicting and managing insect outbreaks.

Area of Science:

  • Ecology
  • Mathematical Biology
  • Forestry

Background:

  • The spruce budworm (Choristoneura fumiferana) is a significant pest affecting spruce-eal forests.
  • Previous mathematical models have been developed to understand budworm population dynamics.

Purpose of the Study:

  • To analyze the dimensionless mathematical model of spruce budworm infestation developed by Ludwig, Jones, and Holling.
  • To investigate how small parameters related to time scales and population mechanisms influence model dynamics.

Main Methods:

  • Analysis of a singular perturbation structure within the mathematical model.
  • Examination of state variable scales and their impact on fast dynamics.
  • Identification of parameter regions corresponding to different dynamic scenarios.

Related Experiment Videos

Main Results:

  • The model exhibits a singular perturbation structure due to disparate time scales (slow and fast).
  • Smaller parameters introduce equilibria at vastly different magnitudes, leading to fast dynamics.
  • Observed dynamics result from a combination of time scale and process scale effects.

Conclusions:

  • The study identifies and analyzes distinct dynamic scenarios within the spruce budworm model.
  • Understanding the interplay of time and process scales is crucial for interpreting model behavior.
  • Parameter space analysis provides insights into the conditions driving different infestation dynamics.