The dynamics of an Omnivore-predator-prey model with harvesting and two different nonlinear functional responses

2019 ◽  
Author(s):  
Salam J. Majeed ◽  
Raid Kamel Naji ◽  
Ashraf Adnan Thirthar
Keyword(s):  
Functional Responses ◽  
Nonlinear Functional ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

A Predator-Prey Model Incorporating Prey Refuge and Allee Effect

2015 ◽  
Vol 713-715 ◽  
pp. 1534-1539 ◽  
Author(s):  
Rui Ning Fan
Keyword(s):  
Time Delay ◽  
Time Lag ◽  
Functional Responses ◽  
Prey Refuge ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Prey Model ◽  
Discrete Time Delay ◽  
Prey Interaction

The effect of refuge used by prey has a stabilizing impact on population dynamics and the effect of time delay has its destabilizing influences. Little attention has been paid to the combined effects of prey refuge and time delay on the dynamic consequences of the predator-prey interaction. Here, a predator-prey model with a class of functional responses was studied by using the analytical approach. The refuge is considered as protecting a constant proportion of prey and the discrete time delay is the gestation period. We evaluated both effects with regard to the local stability of the interior equilibrium point of the considered model. The results showed that the effect of prey refuge has stronger influences than that of time delay on the considered model when the time lag is smaller than the threshold. However, if the time lag is larger than the threshold, the effect of time delay has stronger influences than that of refuge used by prey.

scholarly journals Dynamics of a Diffusive Predator-Prey Model with General Nonlinear Functional Response

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Nonlinear Functional ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Parameter Configuration ◽  
Sufficient And Necessary Conditions ◽  
Steady State Solutions

We study a diffusive predator-prey model with nonconstant death rate and general nonlinear functional response. Firstly, stability analysis of the equilibrium for reduced ODE system is discussed. Secondly, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. Furthermore, sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the system are derived by using the method of Lyapunov function. Finally, we show that there are no nontrivial steady state solutions for certain parameter configuration.

An impulsive two-stage predator–prey model with stage-structure and square root functional responses

2016 ◽  
Vol 119 ◽  
pp. 91-107 ◽  
Author(s):  
Xiangmin Ma ◽  
Yuanfu Shao ◽  
Zhen Wang ◽  
Mengzhuo Luo ◽  
Xianjia Fang ◽  
...  
Keyword(s):  
Stage Structure ◽  
Square Root ◽  
Functional Responses ◽  
Two Stage ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals A hybrid predator–prey model with general functional responses under seasonal succession alternating between Gompertz and logistic growth

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Lei Hang ◽  
Long Zhang ◽  
Xiaowen Wang ◽  
Hongli Li ◽  
Zhidong Teng
Keyword(s):  
Global Attractivity ◽  
Seasonal Succession ◽  
Hybrid Population ◽  
Logistic Growth ◽  
Ultimate Boundedness ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Theoretical Results

AbstractIn this paper, a hybrid predator–prey model with two general functional responses under seasonal succession is proposed. The model is composed of two subsystems: in the first one, the prey follows the Gompertz growth, and it turns to the logistic growth in the second subsystem since seasonal succession. The two processes are connected by impulsive perturbations. Some very general, weak criteria on the ultimate boundedness, permanence, existence, uniqueness and global attractivity of predator-free periodic solution are established. We find that the hybrid population model with seasonal succession has more survival possibilities of natural species than the usual population models. The theoretical results are illustrated by special examples and numerical simulations.

Effects of prey refuges on a predator–prey model with a class of functional responses: The role of refuges

2009 ◽  
Vol 218 (2) ◽  
pp. 73-79 ◽  
Author(s):  
Zhihui Ma ◽  
Wenlong Li ◽  
Yu Zhao ◽  
Wenting Wang ◽  
Hui Zhang ◽  
...  
Keyword(s):  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Prey Refuges

Large deviations for the stochastic predator–prey model with nonlinear functional response

2017 ◽  
Vol 54 (2) ◽  
pp. 507-521 ◽  
Author(s):  
M. Suvinthra ◽  
K. Balachandran
Keyword(s):  
Weak Convergence ◽  
Large Deviations ◽  
Functional Response ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Nonlinear Functional ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Solution Processes ◽  
Prey Model

AbstractIn this paper we consider a diffusive stochastic predator–prey model with a nonlinear functional response and the randomness is assumed to be of Gaussian nature. A large deviation principle is established for solution processes of the considered model by implementing the weak convergence technique.

scholarly journals Global Stability of a Predator-Prey Model with Ivlev-Type Functional Response

2020 ◽  
Vol 99 (99) ◽  
pp. 1-12
Author(s):  
Yinshu Wu ◽  
Wenzhang Huang
Keyword(s):  
Global Stability ◽  
Functional Response ◽  
Local Stability ◽  
Positive Equilibrium ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Predator Prey Models ◽  
Global And Local

A predator-prey model with Ivlev-Type functional response is studied. The main purpose is to investigate the global stability of a positive (co-existence) equilibrium, whenever it exists. A recently developed approach shows that for certain classes of models, there is an implicitly defined function which plays an important rule in determining the global stability of the positive equilibrium. By performing a detailed analytic analysis we demonstrate that a crucial property of this implicitly defined function is governed by the local stability of the positive equilibrium, which enable us to show that the global and local stability of the positive equilibrium, whenever it exists, is equivalent. We believe that our approach can be extended to study the global stability of the positive equilibrium for predator-prey models with some other types of functional responses.

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