Effect of mobility and predator switching on the dynamical behavior of a predator-prey model

2020 ◽  
Vol 132 ◽  
pp. 109584
Author(s):  
Jin-Shan Wang ◽  
Yong-Ping Wu ◽  
Li Li ◽  
Gui-Quan Sun
Keyword(s):  
Dynamical Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Predator Switching

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 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.

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.

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.

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.

Study of the interactive effect of prey toxin and optimal foraging strategy on a predator–prey model

2018 ◽  
Vol 11 (04) ◽  
pp. 1850050
Author(s):  
Ya Li
Keyword(s):  
Energy Intake ◽  
Optimal Foraging ◽  
Interactive Effect ◽  
Dynamical Behavior ◽  
Foraging Strategy ◽  
Food Sources ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Optimal Foraging Strategy

The optimal foraging theory predicts that predators choose prey with more net rate of energy intake and less energy costs if there are multiple food sources available. Toxins are found in many species in nature. Those toxins may be produced by prey as self-protection from predatory animals, or come from other sources such as pesticide residue. Therefore, it requires a balance between energy intake and toxicity damage. In order to study the interactive effect of prey toxin and optimal foraging strategy, we construct a predator–prey model with toxin-induced functional response and optimal foraging property. Dynamical analysis shows that the optimal strategy system presents more complex dynamical behavior than the fixed preference system. We conclude that optimal foraging strategy might play a key role in stabilizing or destabilizing the coexistence states of the species in the system, depending on the level of prey toxins.

Dynamical behavior of a stochastic predator-prey model with stage structure for prey

2020 ◽  
Vol 38 (4) ◽  
pp. 647-667
Author(s):  
Qun Liu ◽  
Daqing Jiang ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Dynamical Behavior ◽  
Stage Structure ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model
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