scholarly journals The Effects of Resource Limitation on a Predator-Prey Model with Control Measures as Nonlinear Pulses

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Wenjie Qin ◽  
Sanyi Tang ◽  
Robert A. Cheke
Keyword(s):  
Natural Enemies ◽  
Dynamical Behavior ◽  
Rank Correlation ◽  
Resource Limitation ◽  
Latin Hypercube Sampling ◽  
Threshold Value ◽  
Control Measures ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

The dynamical behavior of a Holling II predator-prey model with control measures as nonlinear pulses is proposed and analyzed theoretically and numerically to understand how resource limitation affects pest population outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given. Latin hypercube sampling/partial rank correlation coefficients are used to perform sensitivity analysis for the threshold concerning pest extinction to determine the significance of each parameter. Comparing this threshold value with that without resource limitation, our results indicate that it is essential to increase the pesticide’s efficacy against the pest and reduce its effectiveness against the natural enemy, while enhancing the efficiency of the natural enemies. Once the threshold value exceeds a critical level, both pest and its natural enemies populations can oscillate periodically. Further-more, when the pulse period and constant stocking number as a bifurcation parameter, the predator-prey model reveals complex dynamics. In addition, numerical results are presented to illustrate the feasibility of our main results.

scholarly journals Generalized Predator-Prey Model with Nonlinear Impulsive Control Strategy

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wenjie Qin ◽  
Guangyao Tang ◽  
Sanyi Tang
Keyword(s):  
Pest Control ◽  
Impulsive Control ◽  
Dynamical Behavior ◽  
Limited Resource ◽  
Control Measures ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Pest Outbreaks ◽  
Wide Range

A generalized predator-prey model concerning integrated pest management and nonlinear impulsive control measures is proposed and analyzed. The main purpose is to understand how resource limitation affects the successful pest control and pest outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given firstly. Once the threshold value exceeds a critical level, both pest and its natural enemy populations can oscillate periodically. Secondly, in order to address how the limited resources affect the pest control, as an example the Holling II functional response function is chosen. The numerical results show that predator-prey model with limited resource has complex dynamical behavior. In addition, it is confirmed that the model has the coexistence of pests and natural enemies for a wide range of parameters.

scholarly journals Asymptotic Behavior of a Predator-Prey Model with Allee Threshold Applied to Online Social Network Users’ Data Forwarding

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yaming Zhang ◽  
Yaya Hamadou Koura ◽  
Yanyuan Su
Keyword(s):  
Resource Allocation ◽  
Asymptotic Behavior ◽  
Initial Conditions ◽  
Online Social Network ◽  
Dynamical Behavior ◽  
Threshold Value ◽  
Predator Prey ◽  
Interacting Species ◽  
Predator Prey Model ◽  
Prey Model

We consider a predator-prey relationship in a fair system in which interacting species have different needs of resources to survive. We analyzed qualitatively the outcome of interaction using a modified logistic predator-prey model with Allee threshold in both predator and prey equations. We showed that the system had very rich dynamical behavior as stability around fixed points and periodic solutions could be obtained at certain conditions. Interaction outcome is highly submitted to initial conditions, species behavior, and the threshold applied. Numerical results suggested adapting resource allocation and the threshold value to optimize ecosystem sustainability.

THE EFFECTS OF TIMING OF PULSE SPRAYING AND RELEASING PERIODS ON DYNAMICS OF GENERALIZED PREDATOR-PREY MODEL

2012 ◽  
Vol 05 (01) ◽  
pp. 1250012 ◽  
Author(s):  
CHANGTONG LI ◽  
SANYI TANG
Keyword(s):  
Natural Enemies ◽  
Threshold Value ◽  
Threshold Values ◽  
Predator Prey ◽  
Time Points ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Wide Range ◽  
Existence And Stability

Based on the facts of releasing natural enemies and spraying pesticides at different time points, we propose a generalized predator-prey model with impulsive interventions. The threshold values for the existence and stability of pest eradication periodic solution are provided under the assumptions of releasing natural enemies either more or less frequent than spray. In order to address how the different pulse time points, control tactics affect the pest control (i.e. the threshold value), the Holling Type II Lotka-Volterra predator-prey system, as an example, with impulsive intervention at different time points are investigated carefully. The numerical results show how the threshold values are affected by the factors including instantaneous killing rates of pesticides on pests and natural enemies, the release rate of natural enemies and release constant, timing of pesticide application and timing of release period. Furthermore, it is confirmed that the system has the coexistences of pests and natural enemies for a wide range of parameters and with quite different pest amplitudes.

scholarly journals Dynamical behavior of a stochastic predator-prey model with general functional response and nonlinear jump-diffusion

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xinhong Zhang ◽  
Qing Yang
Keyword(s):  
Functional Response ◽  
Dynamical Behavior ◽  
Uniform Boundedness ◽  
Jump Diffusion ◽  
Necessary Condition ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
A New Technique ◽  
The One

<p style='text-indent:20px;'>In this paper, we consider a stochastic predator-prey model with general functional response, which is perturbed by nonlinear Lévy jumps. Firstly, We show that this model has a unique global positive solution with uniform boundedness of <inline-formula><tex-math id="M1">\begin{document}$ \theta\in(0,1] $\end{document}</tex-math></inline-formula>-th moment. Secondly, we obtain the threshold for extinction and exponential ergodicity of the one-dimensional Logistic system with nonlinear perturbations. Then based on the results of Logistic system, we introduce a new technique to study the ergodic stationary distribution for the stochastic predator-prey model with general functional response and nonlinear jump-diffusion, and derive the sufficient and almost necessary condition for extinction and ergodicity.</p>

scholarly journals The Dynamics of a Delayed Predator-Prey Model with Double Allee Effect

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Boli Xie ◽  
Zhijun Wang ◽  
Yakui Xue ◽  
Zhenmin Zhang
Keyword(s):  
Time Delay ◽  
Allee Effect ◽  
Spatial Dynamics ◽  
Threshold Value ◽  
Positive Equilibrium ◽  
Spatiotemporal Model ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Turing Structures

We study the dynamics of a delayed predator-prey model with double Allee effect. For the temporal model, we showed that there exists a threshold of time delay in predator-prey interactions; when time delay is below the threshold value, the positive equilibriumE∗is stable. However, when time delay is above the threshold value, the positive equilibriumE∗is unstable and period solution will emerge. For the spatiotemporal model, through numerical simulations, we show that the model dynamics exhibit rich parameter space Turing structures. The obtained results show that this system has rich dynamics; these patterns show that it is useful for a delayed predator-prey model with double Allee effect to reveal the spatial dynamics in the real model.

scholarly journals Dynamics of a Predator-Prey Model with Fear Effect and Time Delay

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Junli Liu ◽  
Pan Lv ◽  
Bairu Liu ◽  
Tailei Zhang
Keyword(s):  
Numerical Simulations ◽  
Dynamical Behavior ◽  
Normal Form Theory ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Predator Prey Model ◽  
Prey Model ◽  
Delay Dependent ◽  
The Impact ◽  
Dependent Factor

In this paper, we propose a time-delayed predator-prey model with Holling-type II functional response, which incorporates the gestation period and the cost of fear into prey reproduction. The dynamical behavior of this system is both analytically and numerically investigated from the viewpoint of stability, permanence, and bifurcation. We found that there are stability switches, and Hopf bifurcations occur when the delay τ passes through a sequence of critical values. The explicit formulae which determine the direction, stability, and other properties of the bifurcating periodic solutions are given by using the normal form theory and center manifold theorem. We perform extensive numerical simulations to explore the impact of some important parameters on the dynamics of the system. Numerical simulations show that high levels of fear have a stabilizing effect while relatively low levels of fear have a destabilizing effect on the predator-prey interactions which lead to limit-cycle oscillations. We also found that the model with or without a delay-dependent factor can have a significantly different dynamics. Thus, ignoring the delay or not including the delay-dependent factor might result in inaccurate modelling predictions.

Stationary Patterns of a Predator–Prey Model with Prey-Stage Structure and Prey-Taxis

2021 ◽  
Vol 31 (03) ◽  
pp. 2150038
Author(s):  
Meijun Chen ◽  
Huaihuo Cao ◽  
Shengmao Fu
Keyword(s):  
Stage Structure ◽  
Threshold Value ◽  
Turing Instability ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Self Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
Stability And Instability ◽  
Negative Constant

In this paper, a predator–prey model with prey-stage structure and prey-taxis is proposed and studied. Firstly, the local stability of non-negative constant equilibria is analyzed. It is shown that non-negative equilibria have the same stability between ODE system and self-diffusion system, and self-diffusion does not have a destabilization effect. We find that there exists a threshold value [Formula: see text] such that the positive equilibrium point of the model becomes unstable when the prey-taxis rate [Formula: see text], hence the taxis-driven Turing instability occurs. Furthermore, by applying Crandall–Rabinowitz bifurcation theory, the existence, the stability and instability, and the turning direction of bifurcating steady state are investigated in detail. Finally, numerical simulations are provided to support the mathematical analysis.

DYNAMICS OF A DIFFUSIVE PREDATOR–PREY MODEL WITH ADDITIVE ALLEE EFFECT

2012 ◽  
Vol 05 (02) ◽  
pp. 1250023 ◽  
Author(s):  
YONGLI CAI ◽  
WEIMING WANG ◽  
JINFENG WANG
Keyword(s):  
Allee Effect ◽  
Dynamical Behavior ◽  
Positive Equilibrium ◽  
Global Asymptotical Stability ◽  
Allee Effects ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Holling Ii Functional Response

In this paper, we investigate the dynamics of a diffusive predator–prey model with Holling-II functional response and the additive Allee effect in prey. We show the local and global asymptotical stability of the positive equilibrium, and give the conditions of the existence of the Hopf bifurcation. By carrying out global qualitative and bifurcation analysis, it is shown that the weak and strong Allee effects in prey can induce different dynamical behavior in the predator–prey model. Furthermore, we use some numerical simulations to illustrate the dynamics of the model. The results may be helpful for controlling and managing the predator–prey system.

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