Related Experiment Video
Updated: May 12, 2026
06:25
A Real-Time Interactive System for Studying Confrontational Pursuit Behavior in Rodents
Published on: May 16, 2025
Absolute stability and dynamical stabilisation in predator-prey systems
Ayawoa S Dagbovie1, Jonathan A Sherratt
1Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK, ad195@hw.ac.uk.
Journal of Mathematical Biology
|April 11, 2013
Summary
Ecological invasions can show complex patterns due to multi-year cycles. This study explains how dynamical stabilization, a phenomenon where unstable states persist, affects invasion dynamics in cyclic predator-prey systems.
Area of Science:
- Ecology
- Mathematical Biology
- Theoretical Ecology
Background:
- Many ecological systems exhibit multi-year cycles, leading to complex invasion dynamics.
- Unstable steady states can persist as long-term transients behind invasion fronts, a phenomenon termed dynamical stabilization.
Purpose of the Study:
- To predict how the width of the dynamically stabilized region depends on parameter values.
- To analyze invasion dynamics in cyclic predator-prey models.
Main Methods:
- Utilizing absolute stability theory.
- Employing computational methods to analyze model parameters.
Main Results:
- The study predicts the dependence of the stabilized region's width on various parameter values.
- Identified a region of dynamical stabilization separating the invasion front from spatiotemporal oscillations in a cyclic predator-prey model.
Conclusions:
- Dynamical stabilization plays a crucial role in the spatiotemporal structure of invasions in cyclic ecological systems.
- The findings provide insights into the persistence of unstable states and their impact on ecological dynamics.
Related Concept Videos
02:39Predator-Prey Interactions
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.
00:57Population 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.
01:28Stability
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...
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...
01:13Stability of Equilibrium Configuration: Problem Solving
The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
Problem-solving in the context of the stability of equilibrium configuration...
01:23Stability 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...
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...
01:04Oscillations about an Equilibrium Position
Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...