Related Experiment Video
Updated: May 19, 2026
06:25
A Real-Time Interactive System for Studying Confrontational Pursuit Behavior in Rodents
Published on: May 16, 2025
On the Neimark-Sacker bifurcation in a discrete predator-prey system
A N W Hone1, M V Irle, G W Thurura
1Isaac Newton Institute, 20 Clarkson Road, Cambridge, CB3 0EH, UK. anwh@kent.ac.uk
Journal of Biological Dynamics
|August 14, 2012
Summary
This study examines a generalized predator-prey model, revealing a stable steady state and complex dynamics like the Neimark-Sacker bifurcation. The model exhibits richer population behaviors than previous versions.
Area of Science:
- Ecology
- Mathematical Biology
- Dynamical Systems
Background:
- Predator-prey models are fundamental in ecology.
- The Nicholson-Bailey model is a classic discrete-time predator-prey model.
- Previous generalizations showed limited population dynamics.
Purpose of the Study:
- To analyze a two-parameter family of discrete predator-prey models.
- To explore behaviors beyond extinction or unbounded growth.
- To identify conditions for stable nontrivial steady states and bifurcations.
Main Methods:
- Analysis of a system of two coupled nonlinear difference equations.
- Determination of parameter ranges for steady-state stability.
- Investigation of Neimark-Sacker bifurcation conditions.
Main Results:
- A generalized model exhibiting a wider range of behaviors was analyzed.
- A stable nontrivial steady state was identified for specific parameter values.
- The model demonstrates Neimark-Sacker bifurcations, creating attracting or repelling invariant curves.
Conclusions:
- The generalized predator-prey model offers a richer understanding of population dynamics.
- Parameter analysis reveals conditions for stable coexistence and complex oscillatory behaviors.
- Bifurcation analysis highlights the potential for diverse ecological outcomes.
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.
01:28Microbial Interactions: Predation
Microbial predation refers to the process by which one microorganism kills and consumes another to obtain nutrients and energy. It encompasses both bacterial and protozoan predators. This interaction plays a crucial role in shaping microbial communities and regulating nutrient cycling.Bacterial Predators: Epibiotic vs. EndobioticBacterial predators are classified based on their mode of attack as either epibiotic or endobiotic. Epibiotic predators, such as Vampirococcus, attach to the surface of...
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.
00:48Optimal Foraging
How animals obtain and eat their food is called foraging behavior. Foraging can include searching for plants and hunting for prey and depends on the species and environment.
00:58Symbiosis
Symbiotic relationships are long-term, close interactions between individuals of different species that affect the distribution and abundance of those species. When a relationship is beneficial to both species, this is called mutualism. When the relationship is beneficial to one species but neither beneficial nor harmful to the other species, this is called commensalism. When one organism is harmed to benefit another, the relationship is known as parasitism. These types of relationships often...
01:38Limits to Natural Selection
Organisms that are well-adapted to their environment are more likely to survive and reproduce. However, natural selection does not lead to perfectly adapted organisms. Several factors constrain natural selection.