Related Experiment Video
Updated: Mar 2, 2026
06:25
A Real-Time Interactive System for Studying Confrontational Pursuit Behavior in Rodents
Published on: May 16, 2025
1.5K
Dynamics analysis of a delayed reaction-diffusion predator-prey system with non-continuous threshold harvesting
Xuebing Zhang1, Hongyong Zhao2
1Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People's Republic of China; Department of Basic Courses, Huaian Vocational College of Information Technology, Huaian 223003, People's Republic of China.
Mathematical Biosciences
|May 23, 2017
Summary
This study analyzes a delayed predator-prey model with harvesting, exploring stability and bifurcation phenomena. It establishes conditions for equilibrium stability and various bifurcations, validated by numerical simulations.
Area of Science:
- Mathematical Biology
- Ecology
- Dynamical Systems
Background:
- Predator-prey models are fundamental in ecology.
- Delayed differential equations and reaction-diffusion systems capture complex ecological dynamics.
- Threshold harvesting introduces non-linearity and can significantly alter population stability.
Purpose of the Study:
- To investigate the stability and bifurcation properties of a delayed reaction-diffusion predator-prey model with non-continuous threshold harvesting.
- To determine conditions for local and global stability of equilibria.
- To analyze the occurrence of Hopf, Turing, and boundary node bifurcations.
Main Methods:
- Analysis of the characteristic equation for local stability and Hopf/Turing bifurcations.
- Application of the upper-lower solution method for global asymptotic stability of the regular equilibrium.
- Utilization of Lyapunov functions for asymptotic stability of the pseudoequilibrium.
- Study of boundary node bifurcations.
Main Results:
- Sufficient conditions for local stability of the regular equilibrium were derived.
- Conditions for the existence of Hopf and Turing bifurcations were established.
- Global asymptotic stability of the unique regular equilibrium and asymptotic stability of the unique pseudoequilibrium were proven.
- Boundary node bifurcations were investigated.
Conclusions:
- The model exhibits complex dynamics including stability and various bifurcations under threshold harvesting.
- Theoretical findings on stability and bifurcations are supported by numerical simulations.
- The study provides insights into the ecological implications of harvesting strategies in predator-prey systems.
Keywords:
DelayHopf bifurcationNon-continuous harvestingPredator-prey systemReaction-diffusionStabilityMore Related Videos
Related Concept Videos
00:57Population Growth
29.2K
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.
29.2K
02:39Predator-Prey Interactions
21.9K
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.
21.9K
01:25Modeling with Differential Equations
131
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...
131
00:48Optimal Foraging
14.1K
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.
14.1K
01:27Growth Models with Integration: Problem Solving
82
In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
82
01:13Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model
377
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
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,...
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,...
377