scholarly journals Complex Dynamics of a Stochastic Two-Patch Predator-Prey Population Model with Ratio-Dependent Functional Responses

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-31
Author(s):  
Rong Liu ◽  
Guirong Liu
Keyword(s):  
Population Model ◽  
Complex Dynamics ◽  
Sufficient Conditions ◽  
Stochastic Comparison ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Long Time ◽  
Global Positive Solution ◽  
Ratio Dependent

This paper investigates a stochastic two-patch predator-prey model with ratio-dependent functional responses. First, the existence of a unique global positive solution is proved via the stochastic comparison theorem. Then, two different methods are used to discuss the long-time properties of the solutions pathwise. Next, sufficient conditions for extinction and persistence in mean are obtained. Moreover, stochastic persistence of the model is discussed. Furthermore, sufficient conditions for the existence of an ergodic stationary distribution are derived by a suitable Lyapunov function. Next, we apply the main results in some special models. Finally, some numerical simulations are introduced to support the main results obtained. The results in this paper generalize and improve the previous related results.

The Permanence of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control

2013 ◽  
Vol 765-767 ◽  
pp. 327-330
Author(s):  
Chang You Wang ◽  
Xiang Wei Li ◽  
Hong Yuan
Keyword(s):  
Feedback Control ◽  
Sufficient Conditions ◽  
Functional Responses ◽  
Feedback Controls ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Analysis Technique ◽  
Ratio Dependent

This paper is concerned with a Lotka-Volterra predator-prey system with ratio-dependent functional responses and feedback controls. By developing a new analysis technique, we establish the sufficient conditions which guarantee the permanence of the model.

scholarly journals Permanence and global stability of positive solutions of a nonautonomous discrete ratio-dependent predator-prey model

2005 ◽  
Vol 2005 (2) ◽  
pp. 135-144 ◽  
Author(s):  
Hai-Feng Huo ◽  
Wan-Tong Li
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Positive Solution ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

We first give sufficient conditions for the permanence of nonautonomous discrete ratio-dependent predator-prey model. By linearization of the model at positive solutions and construction of Lyapunov function, we also obtain some conditions which ensure that a positive solution of the model is stable and attracts all positive solutions.

Dynamics of a Discrete Prey–Predator Model with Mixed Functional Response

2019 ◽  
Vol 29 (14) ◽  
pp. 1950199
Author(s):  
Mohammed Fathy Elettreby ◽  
Aisha Khawagi ◽  
Tamer Nabil
Keyword(s):  
Type I ◽  
Time Behavior ◽  
Stable Fixed Point ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Long Time ◽  
Predator Model ◽  
The Stability

In this paper, we propose a discrete Lotka–Volterra predator–prey model with Holling type-I and -II functional responses. We investigate the stability of the fixed points of this model. Also, we study the effects of changing each control parameter on the long-time behavior of the model. This model contains a lot of complex dynamical behaviors ranging from a stable fixed point to chaotic attractors. Finally, we illustrate the analytical results by some numerical simulations.

Dynamics of a stochastic Holling II predator-prey model with Lévy jumps and habitat complexity

2021 ◽  
pp. 2150077
Author(s):  
Guangjie Li ◽  
Qigui Yang
Keyword(s):  
Positive Solution ◽  
Habitat Complexity ◽  
Sufficient Conditions ◽  
Ultimate Boundedness ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Global Positive Solution ◽  
Lévy Jumps ◽  
Lyapunov Technique

This paper investigates a stochastic Holling II predator-prey model with Lévy jumps and habit complexity. It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique, and the stochastic ultimate boundedness of this positive solution is also obtained. Sufficient conditions are established for the extinction and persistence of this solution. Moreover, some numerical simulations are carried out to support the obtained results.

Analysis of a stochastic predator–prey model with prey subject to disease and Lévy noise

2019 ◽  
Vol 19 (05) ◽  
pp. 1950038
Author(s):  
Meihong Qiao ◽  
Shenglan Yuan
Keyword(s):  
Positive Solution ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Lévy Noise ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Stochastic Boundedness ◽  
Prey Model ◽  
Global Positive Solution ◽  
Levy Noise

We consider a non-autonomous predator–prey model, with prey subject to the disease and Lévy noise. We show the existence of global positive solution and stochastic boundedness. Then, we examine the asymptotic properties of the solution. Finally, we offer sufficient conditions for persistence and extinction.

scholarly journals Periodic solutions and stability for a delayed discrete ratio-dependent predator-prey system with Holling-type functional response

2004 ◽  
Vol 2004 (2) ◽  
pp. 325-343 ◽  
Author(s):  
Lin-Lin Wang ◽  
Wan-Tong Li
Keyword(s):  
Periodic Solutions ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Globally Asymptotical Stability ◽  
Ratio Dependent

The existence of positive periodic solutions for a delayed discrete predator-prey model with Holling-type-III functional responseN1(k+1)=N1(k)exp{b1(k)−a1(k)N1(k−[τ1])−α1(k)N1(k)N2(k)/(N12(k)+m2N22(k))},N2(k+1)=N2(k)exp{−b2(k)+α2(k)N12(k−[τ2])/(N12(k−[τ2])+m2N22(k−[τ2]))}is established by using the coincidence degree theory. We also present sufficient conditions for the globally asymptotical stability of this system when all the delays are zero. Our investigation gives an affirmative exemplum for the claim that the ratio-dependent predator-prey theory is more reasonable than the traditional prey-dependent predator-prey theory.

RATIO-DEPENDENT PREDATOR–PREY MODEL WITH STAGE STRUCTURE AND TIME DELAY

2012 ◽  
Vol 05 (04) ◽  
pp. 1250014 ◽  
Author(s):  
LIJUAN ZHA ◽  
JING-AN CUI ◽  
XUEYONG ZHOU
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Positive Equilibrium ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent ◽  
Predator Prey Models

Ratio-dependent predator–prey models are favored by many animal ecologists recently as more suitable ones for predator–prey interactions where predation involves searching process. In this paper, a ratio-dependent predator–prey model with stage structure and time delay for prey is proposed and analyzed. In this model, we only consider the stage structure of immature and mature prey species and not consider the stage structure of predator species. We assume that the predator only feed on the mature prey and the time for prey from birth to maturity represented by a constant time delay. At first, we investigate the permanence and existence of the proposed model and sufficient conditions are derived. Then the global stability of the nonnegative equilibria are derived. We also get the sufficient criteria for stability switch of the positive equilibrium. Finally, some numerical simulations are carried out for supporting the analytic results.

scholarly journals Complex Dynamics of a Ratio-Dependent Predator-Prey Model Induced by Spatial Motion

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Caiyun Wang ◽  
Jing Li ◽  
Ruiqiang He
Keyword(s):  
Complex Dynamics ◽  
Intrinsic Factor ◽  
Spatial Effects ◽  
Spatial Motion ◽  
Stripe Pattern ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent ◽  
Predator Prey Models

One of the most efficient predator-prey models with spatial effects is the one with ratio-dependent functional response. However, there is a need to further explore the effects of spatial motion on the dynamic behavior of population. In this work, we study a ratio-dependent predator-prey model with diffusion terms. The aim of this work is to investigate the changes in predator’s distribution in space as the prey populations change their mobility. We observe that the frequency diffusion of the prey gives rise to the sparse density of the predator. Moreover, we also observe that the increasing rate of the conversion into predator biomass induces pattern transitions of the predator. Specifically speaking, Turing pattern of the predator populations goes gradually from a spotted pattern to a black-eye pattern, with the intermediate state being the mixture of spot and stripe pattern. The simulation results and analysis of this work illustrate that the diffusion rate and the real intrinsic factor influence the persistence of the predator-prey system mutually.

scholarly journals Dynamics Analysis of a Stochastic Leslie–Gower Predator-Prey Model with Feedback Controls

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Huailan Ren ◽  
Wencai Zhao
Keyword(s):  
Lyapunov Functions ◽  
Type Ii ◽  
Functional Responses ◽  
Feedback Controls ◽  
Predator Prey ◽  
Noise Interference ◽  
Predator Prey Model ◽  
Prey Model ◽  
Global Positive Solution ◽  
Theoretical Results

This study focuses on the investigation of a stochastic Leslie–Gower predator-prey model with feedback controls and Holling type II functional responses. First, the existence and uniqueness of a global positive solution to the system under white noise interference are proved. Second, the conditions for the existence of the system’s positive recurrence are established by constructing suitable Lyapunov functions. Additionally, the persistence and extinction of prey and predator in the system are discussed, and the impacts of noise interference and feedback controls on the system are revealed. Finally, we validate the theoretical results by numerical simulations.

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