scholarly journals Stability properties of a delayed HIV model with nonlinear functional response and absorption effect

2015 ◽  
Vol 43 (3) ◽  
pp. 235 ◽  
Author(s):  
BG Sampath Aruna Pradeep ◽  
Wanbiao Ma ◽  
Songbai Guo
Keyword(s):  
Functional Response ◽  
Absorption Effect ◽  
Hiv Model ◽  
Nonlinear Functional ◽  
Stability Properties

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.

scholarly journals The Existence and Uniqueness of the Solution of a Diusive Predator-Prey Model with Omnivory and General Nonlinear Functional Response

2021 ◽  
pp. 14-25
Author(s):  
Wensheng Yang
Keyword(s):  
Population Size ◽  
Functional Response ◽  
Carrying Capacity ◽  
Existence And Uniqueness ◽  
Nonlinear Functional ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Uniqueness Of The Solution ◽  
Biotic Resource ◽  
Food Web Model

In this work, we consider a three species modified Lesie-Gower food web model with general  nonlinear functional response and omnivory which is defined as feeding on more than one trophic level. The carrying capacity of the model is proportional to the population size of the biotic resource plus a const. The main objective of this paper is to investigate the existence and  uniqueness of the solution of this model. It is shown that the omnivory has important influence on the existence and uniqueness of the solution of the model.

scholarly journals Permanence of Periodic Predator-Prey System with General Nonlinear Functional Response and Stage Structure for Both Predator and Prey

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Xuming Huang ◽  
Xiangzeng Kong ◽  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Stage Structure ◽  
Functional Responses ◽  
Nonlinear Functional ◽  
Predator Prey ◽  
Prey System

We study the permanence of periodic predator-prey system with general nonlinear functional responses and stage structure for both predator and prey and obtain that the predator and the prey species are permanent.

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 A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Assane Savadogo ◽  
Boureima Sangaré ◽  
Hamidou Ouedraogo
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Functional Response ◽  
Mathematical Analysis ◽  
Existence And Uniqueness ◽  
Nonlinear Functional ◽  
Uniqueness Of The Solution ◽  
Nontrivial Periodic Solutions ◽  
Predator Model ◽  
Stability Results

AbstractIn this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings.

scholarly journals Asymptotic behavior of a stochastic HIV model with Beddington–DeAngelis functional response

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Suxia Wang ◽  
Juan Zhao ◽  
Junxing Zhu ◽  
Xiaoli Ren
Keyword(s):  
Asymptotic Behavior ◽  
Steady State ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Functional Response ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Hiv Model ◽  
Stochastically Stable ◽  
Global Positive Solution

Abstract In this paper, we study the dynamics property of a stochastic HIV model with Beddington–DeAngelis functional response. It has a unique uninfected steady state. We prove that the model has a unique global positive solution. Furthermore, if the basic reproductive number is not larger than 1, the asymptotic behavior of the solution is stochastically stable. Otherwise, it fluctuates randomly around the infected steady state of the corresponding deterministic HIV model. Finally, some numerical simulations are carried out to verify our results.

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