scholarly journals On the Dynamics of a Nonautonomous Predator-Prey Model with Hassell-Varley Type Functional Response

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yan Zhang ◽  
Shujing Gao ◽  
Kuangang Fan
Keyword(s):  
Lyapunov Function ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Incidence Rate ◽  
Functional Response ◽  
Global Attractivity ◽  
Migratory Birds ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model

The dynamic behaviors of a nonautonomous system for migratory birds with Hassell-Varley type functional response and the saturation incidence rate are studied. Under quite weak assumptions, some sufficient conditions are obtained for the permanence and extinction of the disease. Moreover, the global attractivity of the model is discussed by constructing a Lyapunov function. Numerical simulations which support our theoretical analysis are also given.

Dynamical behaviors of a diffusive predator–prey model with Beddington–DeAngelis functional response and disease in the prey

2017 ◽  
Vol 10 (08) ◽  
pp. 1750119 ◽  
Author(s):  
Wensheng Yang
Keyword(s):  
Lyapunov Function ◽  
Iterative Method ◽  
Functional Response ◽  
Local Stability ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Prey Model

The dynamical behaviors of a diffusive predator–prey model with Beddington–DeAngelis functional response and disease in the prey is considered in this work. By applying the comparison principle, linearized method, Lyapunov function and iterative method, we are able to achieve sufficient conditions of the permanence, the local stability and global stability of the boundary equilibria and the positive equilibrium, respectively. Our result complements and supplements some known ones.

EXISTENCE AND GLOBAL ATTRACTIVITY OF A POSITIVE PERIODIC SOLUTION FOR A NON-AUTONOMOUS PREDATOR-PREY MODEL UNDER VIRAL INFECTION

2009 ◽  
Vol 02 (04) ◽  
pp. 419-442 ◽  
Author(s):  
FENGYAN ZHOU
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Lyapunov Function ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Positive Periodic Solution ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

A new non-autonomous predator-prey system with the effect of viruses on the prey is investigated. By using the method of coincidence degree, some sufficient conditions are obtained for the existence of a positive periodic solution. Moreover, with the help of an appropriately chosen Lyapunov function, the global attractivity of the positive periodic solution is discussed. In the end, a numerical simulation is used to illustrate the feasibility of our results.

scholarly journals Permanence and Global Attractivity of Discrete Predator-Prey System with Hassell-Varley Type Functional Response

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Runxin Wu ◽  
Lin Li
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Difference Equation ◽  
Functional Response ◽  
Comparison Theorem ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Prey System

By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the discrete predator-prey system with Hassell-Varley type functional response are obtained. Example together with its numerical simulation shows that the main results are verifiable.

Analysis on stochastic predator-prey model with distributed delay

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
C. Gokila ◽  
M. Sambath
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Disease In Prey ◽  
Stochastic Lyapunov Function

Abstract In the present work, we consider a stochastic predator-prey model with disease in prey and distributed delay. Firstly, we establish sufficient conditions for the extinction of the disease and also permanence of healthy prey and predator. Besides, we obtain the condition for the existence of an ergodic stationary distribution through the stochastic Lyapunov function. Finally, we provide some numerical simulations to validate our theoretical findings.

A Markov-switching predator–prey model with Allee effect for preys

2020 ◽  
Vol 13 (03) ◽  
pp. 2050018
Author(s):  
Xiaoxia Guo ◽  
Zhiming Guo
Keyword(s):  
Numerical Simulations ◽  
Allee Effect ◽  
Global Attractivity ◽  
Markov Switching ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Theoretical Results ◽  
Prey Populations

This paper concerns with a Markov-switching predator–prey model with Allee effect for preys. The conditions under which extinction of predator and prey populations occur have been established. Sufficient conditions are also given for persistence and global attractivity in mean. In addition, stability in the distribution of the system under consideration is derived under some assumptions. Finally, numerical simulations are carried out to illustrate theoretical results.

scholarly journals Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
Jinghui Yang
Keyword(s):  
Lyapunov Function ◽  
Functional Response ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Predator Species ◽  
Predator Prey ◽  
Type Iii ◽  
Prey System ◽  
Ratio Dependent

A ratio-dependent predator-prey system with Holling type III functional response and feedback controls is proposed. By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the system are obtained. After that, under some suitable conditions, we show that the predator speciesywill be driven to extinction. Examples together with their numerical simulations show that the main results are verifiable.

scholarly journals Permanence and Global Attractivity of the Discrete Predator-Prey System with Hassell-Varley-Holling III Type Functional Response

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Runxin Wu ◽  
Lin Li
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Difference Equation ◽  
Functional Response ◽  
Comparison Theorem ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Prey System

By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the discrete predator-prey system with Hassell-Varley-Holling III type functional response are obtained. An example together with its numerical simulation shows that the main results are verifiable.

Extinction and Permanence Analysis of Stochastic Predator-Prey Model with Disease, Ratio-Dependent Type Functional Response and Nonlinear Incidence Rate

2021 ◽  
Author(s):  
Conghui Xu ◽  
Yongguang Yu ◽  
Guojian Ren ◽  
Xudong Hai ◽  
Zhenzhen Lu
Keyword(s):  
Incidence Rate ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Nonlinear Incidence Rate ◽  
Predator Prey ◽  
Nonlinear Incidence ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent ◽  
Dependent Type

Abstract This paper is aimed to investigate a stochastic predator-prey model with disease in both species, which is also considered with ratio-dependent type functional response and nonlinear incidence rate. First, the existence and uniqueness of positive solution is discussed. Then, some sufficient conditions are established to ensure the solution is stochastically ultimate boundedness and permanent. Also, the extinction of susceptible prey, infected prey, susceptible predator and infected predator are analysed, respectively. Furthermore, the boundedness of moments and upper-growth rate estimation are investigated. Finally, numerical simulations are given to illustrate our main results.

scholarly journals Harvesting Control for a Stage-Structured Predator-Prey Model with Ivlev's Functional Response and Impulsive Stocking on Prey

2007 ◽  
Vol 2007 ◽  
pp. 1-15
Author(s):  
Kaiyuan Liu ◽  
Lansun Chen
Keyword(s):  
Functional Response ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
All Solutions ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Delay Differential

We investigate a delayed stage-structured Ivlev's functional response predator-prey model with impulsive stocking on prey and continuous harvesting on predator. Sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system are obtained. These results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactical basis for the biological resource management and enrich the theory of impulsive delay differential equations.

scholarly journals Dynamic behaviors of a nonautonomous predator–prey system with Holling type II schemes and a prey refuge

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yumin Wu ◽  
Fengde Chen ◽  
Caifeng Du
Keyword(s):  
Lyapunov Function ◽  
Differential Equations ◽  
Comparison Theorem ◽  
Sufficient Conditions ◽  
Oscillation Theory ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

AbstractIn this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.

Sign in / Sign up

Export Citation Format

Share Document