scholarly journals Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey Model

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jawdat Alebraheem ◽  
Nasser S. Elazab ◽  
Mogtaba Mohammed ◽  
Anis Riahi ◽  
Ahmed Elmoasry
Keyword(s):  
Initial Conditions ◽  
Dynamical Behavior ◽  
Noise Strength ◽  
Problem Statement ◽  
Stochastic Fluctuation ◽  
Predator Prey ◽  
Prey Model ◽  
Stochastic Fluctuations ◽  
Impacting Factors ◽  
Fluctuation Effects

In this paper, we present new results on deterministic sudden changes and stochastic fluctuations’ effects on the dynamics of a two-predator one-prey model. We purpose to study the dynamics of the model with some impacting factors as the problem statement. The methodology depends on investigating the seasonality and stochastic terms which make the predator-prey interactions more realistic. A theoretical analysis is introduced for studying the effects of sudden deterministic changes, using three different cases of sudden changes. We show that the system in a good situation presents persistence dynamics only as a stable dynamical behavior. However, the system in a bad situation leads to three main outcomes as follows: first, constancy at the initial conditions of the prey and predators; second, extinction of the whole system; third, extinction of both predators, resulting in the growth of the prey population until it reaches a peak carrying capacity. We perform numerical simulations to study effects of stochastic fluctuations, which show that noise strength leads to an increase in the oscillations in the dynamical behavior and became more complex and finally leads to extinction when the strength of the noise is high. The random noises transfer the dynamical behavior from the equilibrium case to the oscillation case, which describes some unstable environments.

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.

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 Simulation of Discrete Predator-Prey Model

2020 ◽  
Vol 55 (1) ◽  
Author(s):  
Adel A. Abed Al Wahab ◽  
Nihad Mahmoud Nasir ◽  
Adil I. Khalil
Keyword(s):  
Discrete Model ◽  
Initial Conditions ◽  
Current Model ◽  
Continuous Model ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Computerized Simulation ◽  
Theoretical Results ◽  
Over Time

It is well known that dynamical systems deal with situations in which the system transforms over time. In fact, undertaking a manual simulation of such systems is a difficult task due to the complexity of the computations. Therefore, a computerized simulation is frequently required for accurate results and fast execution time. Nowadays, computer programs have become an important tool to confirm the theoretical results obtained from the study of models. This paper aims to employ new MATLAB codes to examine a discrete predator–prey model using a difference equations system. The paper discusses the existences and stabilities of each possible fixed point appearing in the current model. Furthermore, numerical simulations fixed by a certain parameter to plot the diagrams are presented. Our results confirm that the systems sensitive to initial conditions are chaotic. Furthermore, the theoretical results as well as numerical examples illustrated that the discrete model exhibits complex behavior compared to a continuous model. The conclusion drawn is that the numerical simulation is an important tool to confirm theoretical results.

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 Paradox of Enrichment in a Stochastic Predator-Prey Model

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jawdat Alebraheem
Keyword(s):  
Initial Conditions ◽  
Random Noise ◽  
Unique Positive Solution ◽  
Predator Prey ◽  
Paradox Of Enrichment ◽  
Predator Prey Model ◽  
Stochastic Boundedness ◽  
Prey Model ◽  
Biological Phenomena ◽  
Theoretical Results

We propose a stochastic predator-prey model to study a novel idea that involves investigating random noises effects on the enrichment paradox phenomenon. Existence and stochastic boundedness of a unique positive solution with positive initial conditions are proved. The global asymptotic stability is studied to determine the occurrence of the enrichment paradox phenomenon. We show theoretically that intensive noises play an important role in the occurrence of the phenomenon, where increasing intensive noises lead to occurrence of the paradox of enrichment. We perform numerical simulations to verify and demonstrate the theoretical results. The new results in this study may contribute to increasing attention to study the random noise effects on some ecological and biological phenomena as the paradox of enrichment.

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.

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