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

Pole and System Stability01:24

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
Separable Differential Equations01:20

Separable Differential Equations

A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
Modeling with Differential Equations01:25

Modeling with Differential Equations

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...
Root Loci for Positive-Feedback Systems01:23

Root Loci for Positive-Feedback Systems

The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
The construction rules for the root locus in positive feedback systems are similar to those in...
Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...

You might also read

Related Articles

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

Sort by
Same author

Treatment outcome in an <i>SI</i> model with evolutionary resistance: a Darwinian model for the evolution of resistance.

Journal of biological dynamics·2023
Same author

A bifurcation theorem for Darwinian matrix models and an application to the evolution of reproductive life-history strategies.

Journal of biological dynamics·2020
Same author

Discrete time darwinian dynamics and semelparity versus iteroparity.

Mathematical biosciences and engineering : MBE·2019
Same author

Predator-prey dynamics of bald eagles and glaucous-winged gulls at Protection Island, Washington, USA.

Ecology and evolution·2019
Same author

Difference equations as models of evolutionary population dynamics.

Journal of biological dynamics·2019
Same author

Periodic matrix models for seasonal dynamics of structured populations with application to a seabird population.

Journal of mathematical biology·2018

Related Experiment Video

Updated: May 19, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Stable bifurcations in semelparous Leslie models.

J M Cushing1, Shandelle M Henson

  • 1Department of Mathematics and Interdisciplinary Program in Applied Mathematics, 617 N Santa Rita, University of Arizona, Tucson, AZ 85721, USA. cushing@math.arizona.edu

Journal of Biological Dynamics
|September 4, 2012
PubMed
Summary

This study analyzes nonlinear Leslie models for semelparous populations. Stability depends on competition intensity: weaker between-class competition promotes stability in forward bifurcations.

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

4D Printed Bifurcated Stents with Kirigami-Inspired Structures
06:52

4D Printed Bifurcated Stents with Kirigami-Inspired Structures

Published on: July 25, 2019

Related Experiment Videos

Last Updated: May 19, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

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

4D Printed Bifurcated Stents with Kirigami-Inspired Structures
06:52

4D Printed Bifurcated Stents with Kirigami-Inspired Structures

Published on: July 25, 2019

Area of Science:

  • Population Dynamics
  • Mathematical Biology
  • Ecology

Background:

  • Semelparous organisms reproduce once, posing unique demographic challenges.
  • Age-structured population models, like Leslie models, are crucial for understanding population dynamics.
  • Understanding stability criteria is vital for predicting population persistence and behavior.

Purpose of the Study:

  • To establish stability and instability criteria for positive equilibria in nonlinear Leslie models for semelparous populations.
  • To analyze the impact of competition intensity on population dynamics.
  • To investigate conditions for dynamic dichotomies, including equilibration and oscillations.

Main Methods:

  • Analysis of nonlinear Leslie models for age-structured populations.
  • Derivation of stability and instability criteria for positive equilibria.
  • Investigation of bifurcations from the extinction equilibrium at R(0)=1.
  • Examination of competition intensities (between-class and within-class).

Main Results:

  • Forward (super-critical) bifurcations lead to stability when between-class competition is weaker than within-class competition.
  • Backward (sub-critical) bifurcations result in unstable equilibria.
  • Criteria were established to determine if the boundary of the positive cone acts as an attractor or repeller.
  • Competition intensity significantly influences population stability and dynamics.

Conclusions:

  • Nonlinear Leslie models reveal complex dynamics in semelparous populations.
  • Competition structure is a key determinant of population stability and potential for oscillations.
  • The findings contribute to understanding dynamic dichotomies in population modeling.