Related Experiment Video
Updated: Nov 29, 2025

A Real-Time Interactive System for Studying Confrontational Pursuit Behavior in Rodents
Published on: May 16, 2025
Dynamical analysis of a delayed diffusive predator-prey model with schooling behaviour and Allee effect
Xin-You Meng1, Jiao-Guo Wang1,2
1School of Science, Lanzhou University of Technology, Lanzhou, People's Republic of China.
This study analyzes a predator-prey model with schooling behavior and Allee effect, revealing complex dynamics. Mathematical analysis and simulations explore how delays and diffusion influence population stability and create bifurcations.
Area of Science:
- Mathematical Biology
- Theoretical Ecology
- Dynamical Systems
Background:
- Predator-prey models are fundamental in ecology.
- Schooling behavior and Allee effects introduce complex population dynamics.
- Time delays and diffusion are crucial factors in ecological modeling.
Purpose of the Study:
- Investigate a delayed diffusive predator-prey model incorporating schooling behavior and Allee effects.
- Analyze the existence and stability of equilibria.
- Examine Hopf bifurcations in both delayed and undelayed systems.
Main Methods:
- Analysis of equilibria and local stability.
- Hopf bifurcation analysis using conversion rate as the bifurcation parameter.
- Application of center manifold and normal form theory for partial functional differential equations.
- Numerical simulations to validate theoretical findings.
Main Results:
- Determined the existence and local stability of equilibria for the non-diffusive, non-delayed model.
- Identified Hopf bifurcations in the diffusive system without time delay.
- Investigated the stability of the coexistent equilibrium and Hopf bifurcations in the presence of time delays.
- Characterized Hopf bifurcation properties using advanced mathematical theories.
Conclusions:
- The delayed diffusive predator-prey model with schooling and Allee effects exhibits rich dynamical behaviors.
- Time delays and diffusion significantly impact population stability and can induce bifurcations.
- Theoretical results are corroborated by numerical simulations, enhancing understanding of ecological interactions.
More Related Videos
20:36Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
09:23Methodology for Developing Life Tables for Sessile Insects in the Field Using the Whitefly, Bemisia tabaci, in Cotton As a Model System
Published on: November 1, 2017
Related Concept Videos
Population Growth
Optimal Foraging
Predator-Prey Interactions
Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
Mechanistic Models: Compartment Models in Individual and Population Analysis
Exponential Equations for Modeling Growth