EFFECT OF ADDITIONAL FOOD ON PREDATOR–PREY INTERACTIONS WITH WATER-LEVEL FLUCTUATION

2021 ◽  
pp. 1-28
Author(s):  
ABHIJIT SARKAR ◽  
PANKAJ KUMAR TIWARI ◽  
SAMARES PAL
Keyword(s):  
Periodic Solution ◽  
Water Level ◽  
Positive Periodic Solution ◽  
Water Level Fluctuations ◽  
Logistic Growth ◽  
Generalist Predator ◽  
Predator Population ◽  
Additional Food ◽  
Predator Prey ◽  
Predator Prey Model

Significant variations of the water-level of the lake can have a strong impact on the persistence of species. Indeed, when the water-level is low, during the autumn, the contact between the predator and the prey is more frequent, and the predation increases. Conversely, when the water-level is high, in the spring, it is more difficult for the predator to find a prey and the predation decreases. In this paper, we consider a seasonally varying predator–prey model to study the influence of water-level variations on the interaction between two species of fishes in an artificial lake. A seasonal variation of the water-level is introduced in the predation rate. The predator population is provided some additional food apart from the focal prey, and follows logistic growth in the absence of prey population. As control upon the over predation, the predator population is harvested. Sensitivity analysis shows that the biomass of predator population is highly sensitive to the additional food and water variations. In the absence of additional food, our results show bursting patterns of fishes whereas positive periodic solution arises if the additional food is available in sufficient amount. The positive periodic solution is shown to be globally stable. Higher values of water-level fluctuations induce double periodic oscillations. Our findings show that providing additional food source to the generalist predator together with water-level fluctuations exerts a strong influence on the interaction between fishes.

A delay nonautonomous model for the effects of fear and refuge on predator–prey interactions with water-level fluctuations

2022 ◽  
Author(s):  
Abhijit Sarkar ◽  
Pankaj Kumar Tiwari ◽  
Samares Pal
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Water Level ◽  
Positive Periodic Solution ◽  
Time Dependent ◽  
Water Level Fluctuations ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Water Level Variations

The interaction of prey (small fish) and predator (large fish) in lakes/ponds at temperate and tropical regions varies when water level fluctuates naturally during seasonal time. We relate the perceptible effect of fear and anti-predator behavior of prey with the water-level fluctuations and describe how these are influenced by the seasonal changing of water level. So, we consider these as time-dependent functions to make the system more realistic. Also, we incorporate the time-dependent delay in the negative growth rate of prey in predator–prey model with Crowley–Martin-type functional response. We clearly provide the basic dynamics of the system such as positiveness, permanence and nonpersistence. The existence of positive periodic solution is studied using Continuation theorem, and suffiecient conditions for globally attractivity of positive periodic solution are also derived. To make the system more comprehensive, we establish numerical simulations, and compare the dynamics of autonomous and nonautonomous systems in the absence as well as the presence of time delay. Our results show that seasonality and time delay create the occurrence of complex behavior such as prevalence of chaotic disorder which can be potentially suppressed by the cost of fear and prey refuge. Also, if time delay increases, then system leads a boundary periodic solution. Our findings assert that the predation, fear of predator and prey refuge are correlated with water-level variations, and give some reasonable biological interpretations for persistence as well as extinction of species due to water-level variations.

scholarly journals On a predator-prey system interaction under fluctuating water level with nonselective harvesting

2020 ◽  
Vol 18 (1) ◽  
pp. 458-475
Author(s):  
Na Zhang ◽  
Yonggui Kao ◽  
Fengde Chen ◽  
Binfeng Xie ◽  
Shiyu Li
Keyword(s):  
Water Level ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Model Interaction ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fluctuating Water Level

Abstract A predator-prey model interaction under fluctuating water level with non-selective harvesting is proposed and studied in this paper. Sufficient conditions for the permanence of two populations and the extinction of predator population are provided. The non-negative equilibrium points are given, and their stability is studied by using the Jacobian matrix. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global stability of the positive equilibrium are obtained. The bionomic equilibrium and the optimal harvesting policy are also presented. Numerical simulations are carried out to show the feasibility of the main results.

scholarly journals The Study of a Predator-Prey Model with Fear Effect Based on State-Dependent Harvesting Strategy

Complexity ◽  
2022 ◽  
Vol 2022 ◽  
pp. 1-19
Author(s):  
Y. Tian ◽  
H. M. Li
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Prey Population ◽  
Global Dynamics ◽  
Predator Population ◽  
Positive Order ◽  
Predator Prey ◽  
Predator Prey Model ◽  
State Dependent ◽  
The Stability

In presence of predator population, the prey population may significantly change their behavior. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. In this study, we propose a predator-prey fishery model introducing the cost of fear into prey reproduction with Holling type-II functional response and prey-dependent harvesting and investigate the global dynamics of the proposed model. For the system without harvest, it is shown that the level of fear may alter the stability of the positive equilibrium, and an expression of fear critical level is characterized. For the harvest system, the existence of the semitrivial order-1 periodic solution and positive order- q ( q ≥ 1 ) periodic solution is discussed by the construction of a Poincaré map on the phase set, and the threshold conditions are given, which can not only transform state-dependent harvesting into a cycle one but also provide a possibility to determine the harvest frequency. In addition, to ensure a certain robustness of the adopted harvest policy, the threshold condition for the stability of the order- q periodic solution is given. Meanwhile, to achieve a good economic profit, an optimization problem is formulated and the optimum harvest level is obtained. Mathematical findings have been validated in numerical simulation by MATLAB. Different effects of different harvest levels and different fear levels have been demonstrated by depicting figures in numerical simulation using MATLAB.

PREDATOR–PREY DYNAMICS WITH SEASONAL WATER-LEVEL FLUCTUATIONS

2018 ◽  
Vol 26 (04) ◽  
pp. 495-510 ◽  
Author(s):  
A. MOUSSAOUI ◽  
M. A. AZIZ-ALAOUI ◽  
S. BASSAID
Keyword(s):  
Water Level ◽  
Great Influence ◽  
Predation Rate ◽  
Water Level Fluctuations ◽  
Water Volume ◽  
Artificial Lake ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Influence Of Water ◽  
Lakes And Reservoirs

Water level in rivers, lakes and reservoirs has great influence on the interactions between prey and predator fish. Indeed, the increase of the water volume hinders the capture of the prey by the predator. The same reasoning applies when there is a decrease in the volume of water, favoring the capture of the prey by the predator. In this paper, we consider a seasonally varying predator–prey model to study the influence of water-level variations on the interaction between two species of fishes in an artificial lake. A seasonal variation of the water-level is introduced in the predation rate taking into account two values, leading to a general switched system. Permanence, stability and existence of an invariant domain containing at least one periodic solution are established. Our theoretical results confirm the assumption that the water exerts a strong influence on the interaction between fishes.

THE ROLE OF ADDITIONAL FOOD IN A PREDATOR–PREY MODEL WITH A PREY REFUGE

2016 ◽  
Vol 24 (02n03) ◽  
pp. 345-365 ◽  
Author(s):  
SUDIP SAMANTA ◽  
RIKHIYA DHAR ◽  
IBRAHIM M. ELMOJTABA ◽  
JOYDEV CHATTOPADHYAY
Keyword(s):  
Stable Equilibrium ◽  
Predator Population ◽  
Stable Limit ◽  
Prey Refuge ◽  
Additional Food ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Stability ◽  
The Impact

In this paper, we propose and analyze a predator–prey model with a prey refuge and additional food for predators. We study the impact of a prey refuge on the stability dynamics, when a constant proportion or a constant number of prey moves to the refuge area. The system dynamics are studied using both analytical and numerical techniques. We observe that the prey refuge can replace the predator–prey oscillations by a stable equilibrium if the refuge size crosses a threshold value. It is also observed that, if the refuge size is very high, then the extinction of the predator population is certain. Further, we observe that enhancement of additional food for predators prevents the extinction of the predator and also replaces the stable limit cycle with a stable equilibrium. Our results suggest that additional food for the predators enhances the stability and persistence of the system. Extensive numerical experiments are performed to illustrate our analytical findings.

EXISTENCE AND GLOBAL ATTRACTIVITY OF A POSITIVE PERIODIC SOLUTION FOR A NON-AUTONOMOUS PREDATOR-PREY MODEL UNDER VIRAL INFECTION

2009 ◽  
Vol 02 (04) ◽  
pp. 419-442 ◽  
Author(s):  
FENGYAN ZHOU
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Lyapunov Function ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Positive Periodic Solution ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

A new non-autonomous predator-prey system with the effect of viruses on the prey is investigated. By using the method of coincidence degree, some sufficient conditions are obtained for the existence of a positive periodic solution. Moreover, with the help of an appropriately chosen Lyapunov function, the global attractivity of the positive periodic solution is discussed. In the end, a numerical simulation is used to illustrate the feasibility of our results.

scholarly journals A diffusive predator-prey model with generalist predator and time delay

2021 ◽  
Vol 7 (3) ◽  
pp. 4574-4591
Author(s):  
Ruizhi Yang ◽  
◽  
Dan Jin ◽  
Wenlong Wang
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Resource Limitation ◽  
Generalist Predator ◽  
Center Manifold Reduction ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Stability ◽  
Bifurcating Periodic Solution

<abstract><p>Time delay in the resource limitation of the prey is incorporated into a diffusive predator-prey model with generalist predator. By analyzing the eigenvalue spectrum, time delay inducing instability and Hopf bifurcation are investigated. Some conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution are obtained by utilizing the normal form method and center manifold reduction for partial functional differential equation. The results suggest that time delay can destabilize the stability of coexisting equilibrium and induce bifurcating periodic solution when it increases through a certain threshold.</p></abstract>

scholarly journals Permanence and periodic solution for a modified Leslie-Gower type predator-prey model with diffusion and non constant coefficients

BIOMATH ◽  
2017 ◽  
Vol 6 (1) ◽  
pp. 1707107
Author(s):  
Moussaoui Ali ◽  
M. A. Aziz Alaoui ◽  
R. Yafia
Keyword(s):  
Periodic Solution ◽  
System Modeling ◽  
Sufficient Conditions ◽  
Environmental Parameters ◽  
Positive Periodic Solution ◽  
Auxiliary Function ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Constant Coefficients

In this paper we study a predator-prey system, modeling the interaction of two species with diffusion and T-periodic environmental parameters. It is a Leslie-Gower type predator-prey model with Holling-type-II functional response. We establish some sufficient conditions for the ultimate boundedness of solutions and permanence of this system. By constructing an appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Numerical simulations are presented to illustrate the results.

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