A note on stability of discrete population models

Related Experiment Video

Updated: Sep 29, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
20:36

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Published on: July 3, 2007

Y Huang

    Mathematical Biosciences
    |August 1, 1989
    PubMed

    More Related Videos

    Following the Dynamics of Structural Variants in Experimentally Evolved Populations04:52

    Following the Dynamics of Structural Variants in Experimentally Evolved Populations

    Published on: February 3, 2023

    Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis06:44

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

    Published on: September 23, 2025

    Related Concept Videos

    Population Growth00:57

    Population Growth

    Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.However, realistic environmental conditions limit the number of...
    Stability of Equilibrium Configuration01:23

    Stability of Equilibrium Configuration

    Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
    A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
    Stability of structures01:14

    Stability of structures

    In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...
    BIBO stability of continuous and discrete -time systems01:24

    BIBO stability of continuous and discrete -time systems

    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.
    Stability01:28

    Stability

    The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
    The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
    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...