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

Cyclic Processes And Isolated Systems01:19

Cyclic Processes And Isolated Systems

2.9K
A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state. 
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each...
2.9K
Linear time-invariant Systems01:23

Linear time-invariant Systems

357
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
357
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

492
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
492
The Integrated Rate Law: The Dependence of Concentration on Time02:39

The Integrated Rate Law: The Dependence of Concentration on Time

35.8K
While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...
35.8K
Multicompartment Models: Overview01:14

Multicompartment Models: Overview

233
Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
233
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

81
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
81

You might also read

Related Articles

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

Sort by
Same author

Darwinian dynamics of Host-Pathogen interactions.

Mathematical biosciences and engineering : MBE·2026
Same author

A discrete-time continuous-space neural model for shell patterns in mollusks.

Journal of theoretical biology·2025
Same author

Massera's theorem on arbitrary discrete time domains.

Mathematical biosciences and engineering : MBE·2025
Same author

Rapid Evolution of Resistance and Tolerance Leads to Variable Host Recoveries following Disease-Induced Declines.

The American naturalist·2024
Same author

Square root identities for harvested Beverton-Holt models.

Journal of theoretical biology·2022
Same author

Derivation and Analysis of a Discrete Predator-Prey Model.

Bulletin of mathematical biology·2022

Related Experiment Video

Updated: Aug 28, 2025

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
12:03

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

Published on: May 25, 2019

8.5K

The Beverton-Hold model on isolated time scales.

Martin Bohner1, Jaqueline Mesquita2, Sabrina Streipert3

  • 1Missouri S & T, Department of Mathematics and Statistics, Rolla, MO 65409-0020, USA.

Mathematical Biosciences and Engineering : MBE
|September 20, 2022
PubMed
Summary

This study extends the Beverton-Holt population model to isolated time scales, proving a unique periodic solution and an upper bound for population dynamics. These findings address key conjectures and reveal time structure impacts.

Keywords:
Beverton–Holt equationCushing–Henson conjectureisolated time scaleperiodic solutionsperiodicity concept

More Related Videos

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.4K
Author Spotlight: Exploring Light-Driven Chemical Reactions and Energy-Harnessing Devices in Photochemical Research
08:12

Author Spotlight: Exploring Light-Driven Chemical Reactions and Energy-Harnessing Devices in Photochemical Research

Published on: February 16, 2024

10.9K

Related Experiment Videos

Last Updated: Aug 28, 2025

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
12:03

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

Published on: May 25, 2019

8.5K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.4K
Author Spotlight: Exploring Light-Driven Chemical Reactions and Energy-Harnessing Devices in Photochemical Research
08:12

Author Spotlight: Exploring Light-Driven Chemical Reactions and Energy-Harnessing Devices in Photochemical Research

Published on: February 16, 2024

10.9K

Area of Science:

  • Mathematical Biology
  • Dynamical Systems
  • Time Scale Theory

Background:

  • The Beverton-Holt model is a fundamental tool in population dynamics.
  • Existing research primarily focuses on discrete and continuous time scales.
  • Periodicity's impact on population models requires further investigation, especially on generalized time scales.

Purpose of the Study:

  • To formulate and analyze the Beverton-Holt model on isolated time scales.
  • To investigate the effects of periodicity on population dynamics within this framework.
  • To extend and address existing conjectures (Cushing-Henson) in the context of time scales.

Main Methods:

  • Formulation of the Beverton-Holt equation on arbitrary isolated time scales.
  • Application of a novel definition of periodicity for isolated time scales.
  • Development of mathematical theorems to establish existence, uniqueness, stability, and bounds of solutions.

Main Results:

  • Existence and global asymptotic stability of a unique ω-periodic solution, addressing the first Cushing-Henson conjecture.
  • Derivation of an upper bound for the average of the periodic solution, generalizing the second Cushing-Henson conjecture.
  • Demonstration that the upper bound depends on the underlying time scale structure.

Conclusions:

  • The study successfully extends the Beverton-Holt model to isolated time scales, confirming key conjectures.
  • Periodicity significantly influences population dynamics, with effects modulated by the time scale's structure.
  • The findings offer a foundation for applying periodicity concepts to other dynamic models on isolated time scales.