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 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.

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.

Dynamic Analysis of a Stochastic Predator–Prey Model With Crowley–Martin Functional Response, Disease in Predator, and Saturation Incidence

2020 ◽  
Vol 15 (7) ◽  
Author(s):  
Conghui Xu ◽  
Yongguang Yu ◽  
Guojian Ren
Keyword(s):  
Functional Response ◽  
Existence And Uniqueness ◽  
Global Attractivity ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Disease In Predator ◽  
Long Time

Abstract This work aims to study some dynamical properties of a stochastic predator–prey model, which is considered under the combination of Crowley–Martin functional response, disease in predator, and saturation incidence. First, we discuss the existence and uniqueness of positive solution of the concerned stochastic model. Second, we prove that the solution is stochastically ultimate bounded. Then, we investigate the extinction and the long-time behavior of the solution. Furthermore, we establish some conditions for the global attractivity of the model. Finally, we propose some numerical simulations to illustrate our main results.

scholarly journals A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Aziz Khan ◽  
Hashim M. Alshehri ◽  
J. F. Gómez-Aguilar ◽  
Zareen A. Khan ◽  
G. Fernández-Anaya
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Variable Order ◽  
Fractional Order Systems ◽  
New Approach ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Fractional Differential ◽  
The Fixed Point Theorem

AbstractThis paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is generated by using another FO derivative developed as a kernel based on the generalized Mittag-Leffler function. Two fractional-order systems are assumed, with and without delay. For the numerical solution of the models, we not only employ the Adams–Bashforth–Moulton method but also explore the existence and uniqueness of these schemes. We use the fixed point theorem which is useful in describing the existence of a new approach with a particular set of solutions. For the illustration, several numerical examples are added to the paper to show the effectiveness of the numerical method.

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