scholarly journals Analysis of a Predator-Prey Model with Distributed Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Gunasundari Chandrasekar ◽  
Salah Mahmoud Boulaaras ◽  
Senthilkumaran Murugaiah ◽  
Arul Joseph Gnanaprakasam ◽  
Bahri Belkacem Cherif
Keyword(s):  
Distributed Delay ◽  
Nonequilibrium Dynamics ◽  
Global Dynamics ◽  
Well Posedness ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Mean Delay ◽  
Prey Model ◽  
Local And Global Dynamics ◽  
The Mean

In this paper, we consider a predator-prey model, where we assumed that the model to be an infected predator-free equilibrium one. The model includes a distributed delay to describe the time between the predator’s capture of the prey and its conversion to biomass for predators. When the delay is absent, the model exhibits asymptotic convergence to an equilibrium. Therefore, any nonequilibrium dynamics in the model when the delay is included can be attributed to the delay’s inclusion. We assume that the delay is distributed and model the delay using integrodifferential equations. We established the well-posedness and basic properties of solutions of the model with nonspecified delay. Then, we analyzed the local and global dynamics as the mean delay varies.

Bifurcation Analysis and Optimal Harvesting of a Delayed Predator–Prey Model

2015 ◽  
Vol 25 (01) ◽  
pp. 1550012 ◽  
Author(s):  
P. Tchinda Mouofo ◽  
R. Djidjou Demasse ◽  
J. J. Tewa ◽  
M. A. Aziz-Alaoui
Keyword(s):  
Natural Resource Management ◽  
Optimal Control Theory ◽  
Uniform Boundedness ◽  
Optimal Harvesting ◽  
Global Dynamics ◽  
Saddle Node Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Local Bifurcations ◽  
Prey Model

A delay predator–prey model is formulated with continuous threshold prey harvesting and Holling response function of type III. Global qualitative and bifurcation analyses are combined to determine the global dynamics of the model. The positive invariance of the non-negative orthant is proved and the uniform boundedness of the trajectories. Stability of equilibria is investigated and the existence of some local bifurcations is established: saddle-node bifurcation, Hopf bifurcation. We use optimal control theory to provide the correct approach to natural resource management. Results are also obtained for optimal harvesting. Numerical simulations are given to illustrate the results.

Modeling and analysis of a predator–prey model with state-dependent delay

2018 ◽  
Vol 11 (02) ◽  
pp. 1850026 ◽  
Author(s):  
Yunfei Lv ◽  
Yongzhen Pei ◽  
Rong Yuan
Keyword(s):  
Immature Stage ◽  
Global Dynamics ◽  
Modeling And Analysis ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Prey Model ◽  
State Dependent ◽  
State Dependent Delay ◽  
Threshold Amount

We propose and study a predator–prey model with state-dependent delay where the prey population is assumed to have an age structure. The state-dependent delay appears due to the mature condition that the prey must spend an amount of time in the immature stage sufficient to accumulate a threshold amount of food. We perform a qualitative analysis of the solutions, which includes studying positivity and boundedness, existence and local stability of equilibria. For the global dynamics of the system, we discuss an attracting region which is determined by solutions, and the region collapses to the interior equilibrium in the constant delay case.

scholarly journals Global dynamics and parameter identifiability in a predator-prey interaction model

2018 ◽  
Vol 5 (1) ◽  
pp. 113-126
Author(s):  
Jai Prakash Tripathi ◽  
Suraj S. Meghwani ◽  
Swati Tyagi ◽  
Syed Abbas
Keyword(s):  
Interaction Model ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Prey Refuge ◽  
Predator Species ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Prey Model ◽  
Permanence Property

AbstractThis paper discusses a predator-prey model with prey refuge. We investigate the role of prey refuge on the existence and stability of the positive equilibrium. The global asymptotic stability of positive interior equilibrium solution is established using suitable Lyapunov functional, which shows that the prey refuge has no influence on the permanence property of the system. Mathematically, we analyze the effect of increase or decrease of prey reserve on the equilibrium states of prey and predator species. To access the usability of proposed predator-prey model in practical scenarios, we also suggest, the use of Levenberg-Marquardt (LM) method for associated parameter estimation problem. Numerical results demonstrate faithful reconstruction of system dynamics by estimated parameter by LM method. The analytical results found in this paper are illustrated with the help of suitable numerical examples

Persistence and extinction of a stochastic delay predator-prey model in a polluted environment

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
Zhenhai Liu ◽  
Qun Liu
Keyword(s):  
Numerical Simulations ◽  
Critical Value ◽  
Polluted Environment ◽  
Stochastic Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Persistence In The Mean ◽  
The Mean

AbstractIn this paper, we study a stochastic delay predator-prey model in a polluted environment. Sufficient criteria for extinction and non-persistence in the mean of the model are obtained. The critical value between persistence and extinction is also derived for each population. Finally, some numerical simulations are provided to support our main results.

Sign in / Sign up

Export Citation Format

Share Document