scholarly journals Analisis Kestabilan Model Predator-Prey dengan Adanya Faktor Tempat Persembunyian Menggunakan Fungsi Respon Holling Tipe III

2021 ◽  
Vol 3 (2) ◽  
pp. 88
Author(s):  
Riris Nur Patria Putri ◽  
Windarto Windarto ◽  
Cicik Alfiniyah
Keyword(s):  
Numerical Simulation ◽  
Response Function ◽  
Equilibrium Points ◽  
Prey Population ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Asymptotic Stable ◽  
Simulation Results ◽  
Model Predator

Predation is interaction between predator and prey, where predator preys prey. So predators can grow, develop, and reproduce. In order for prey to avoid predators, then prey needs a refuge. In this thesis, a predator-prey model with refuge factor using Holling type III response function which has three populations, i.e. prey population in the refuge, prey population outside the refuge, and predator population. From the model, three equilibrium points were obtained, those are extinction of the three populations which is unstable, while extinction of predator population and coexistence are asymptotic stable under certain conditions. The numerical simulation results show that refuge have an impact the survival of the prey.

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.

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.

A linear birth-and-death predator–prey process

1995 ◽  
Vol 32 (01) ◽  
pp. 274-277
Author(s):  
John Coffey
Keyword(s):  
Death Rate ◽  
Birth Rate ◽  
Prey Population ◽  
Death Process ◽  
Predator Population ◽  
Birth And Death Process ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

A new stochastic predator-prey model is introduced. The predator population X(t) is described by a linear birth-and-death process with birth rate λ 1 X and death rate μ 1 X. The prey population Y(t) is described by a linear birth-and-death process in which the birth rate is λ 2 Y and the death rate is . It is proven that and iff

OCCURRENCE OF CHAOS AND ITS POSSIBLE CONTROL IN A PREDATOR-PREY MODEL WITH DENSITY DEPENDENT DISEASE-INDUCED MORTALITY ON PREDATOR POPULATION

2010 ◽  
Vol 18 (02) ◽  
pp. 399-435 ◽  
Author(s):  
KRISHNA PADA DAS ◽  
SAMRAT CHATTERJEE ◽  
J. CHATTOPADHYAY
Keyword(s):  
Equilibrium Points ◽  
Dynamical Behaviour ◽  
Predator Population ◽  
Epidemiological Models ◽  
Predator Prey ◽  
Density Dependent ◽  
Predator Prey Model ◽  
Chaotic Nature ◽  
Mortality Function ◽  
Infected Prey

Eco-epidemiological models are now receiving much attention to the researchers. In the present article we re-visit the model of Holling-Tanner which is recently modified by Haque and Venturino1 with the introduction of disease in prey population. Density dependent disease-induced predator mortality function is an important consideration of such systems. We extend the model of Haque and Venturino1 with density dependent disease-induced predator mortality function. The existence and local stability of the equilibrium points and the conditions for the permanence and impermanence of the system are worked out. The system shows different dynamical behaviour including chaos for different values of the rate of infection. The model considered by Haque and Venturino1 also exhibits chaotic nature but they did not shed any light in this direction. Our analysis reveals that by controlling disease-induced mortality of predator due to ingested infected prey may prevent the occurrence of chaos.

scholarly journals Predator-prey interactions under fear effect and multiple foraging strategies

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Susmita Halder ◽  
Joydeb Bhattacharyya ◽  
Samares Pal
Keyword(s):  
Complex Dynamics ◽  
Model Simulation ◽  
Prey Population ◽  
Foraging Strategies ◽  
Generalist Predator ◽  
Hopf Bifurcations ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Simulation Results

<p style='text-indent:20px;'>We propose and analyze the effects of a generalist predator-driven fear effect on a prey population by considering a modified Leslie-Gower predator-prey model. We assume that the prey population suffers from reduced fecundity due to the fear of predators. We investigate the predator-prey dynamics by incorporating linear, Holling type Ⅱ and Holling type Ⅲ foraging strategies of the generalist predator. As a control strategy, we have considered density-dependent harvesting of the organisms in the system. We show that the systems with linear and Holling type Ⅲ foraging exhibit transcritical bifurcation, whereas the system with Holling type Ⅱ foraging has a much more complex dynamics with transcritical, saddle-node, and Hopf bifurcations. It is observed that the prey population in the system with Holling type Ⅲ foraging of the predator gets severely affected by the predation-driven fear effect in comparison with the same with linear and Holling type Ⅱ foraging rates of the predator. Our model simulation results show that an increase in the harvesting rate of the predator is a viable strategy in recovering the prey population.</p>

scholarly journals Dynamics of a Predator-Prey Population in the Presence of Resource Subsidy under the Influence of Nonlinear Prey Refuge and Fear Effect

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-38
Author(s):  
Sudeshna Mondal ◽  
G. P. Samanta ◽  
Juan J. Nieto
Keyword(s):  
Equilibrium Points ◽  
Time Lag ◽  
Sufficient Conditions ◽  
Food Sources ◽  
Prey Population ◽  
Predator Population ◽  
Input Rate ◽  
Prey Refuge ◽  
Predator Prey ◽  
The Impact

In this work, our aim is to investigate the impact of a non-Kolmogorov predator-prey-subsidy model incorporating nonlinear prey refuge and the effect of fear with Holling type II functional response. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). The positivity and asymptotically uniform boundedness of the solutions of the system have been derived. Analytically, we have studied the criteria for the feasibility and stability of different equilibrium points. In addition, we have derived sufficient conditions for the existence of local bifurcations of codimension 1 (transcritical and Hopf bifurcation). It is also observed that there is some time lag between the time of perceiving predator signals through vocal cues and the reduction of prey’s birth rate. So, we have analyzed the dynamical behaviour of the delayed predator-prey-subsidy model. Numerical computations have been performed using MATLAB to validate all the analytical findings. Numerically, it has been observed that the predator, prey, and subsidy can always exist at a nonzero subsidy input rate. But, at a high subsidy input rate, the prey population cannot persist and the predator population has a huge growth due to the availability of food sources.

A mathematical study of a predator–prey model with disease circulating in the both populations

2015 ◽  
Vol 08 (02) ◽  
pp. 1550015 ◽  
Author(s):  
Krishna Pada Das ◽  
J. Chattopadhyay
Keyword(s):  
Equilibrium Point ◽  
Prey Population ◽  
Global Dynamics ◽  
Predator Population ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Force Of Infection ◽  
Predator Prey Model ◽  
High Infection ◽  
Infected Prey

Disease in ecological systems plays an important role. In the present investigation we propose and analyze a predator–prey mathematical model in which both species are affected by infectious disease. The parasite is transmitted directly (by contact) within the prey population and indirectly (by consumption of infected prey) within the predator population. We derive biologically feasible and insightful quantities in terms of ecological as well as epidemiological reproduction numbers that allow us to describe the dynamics of the proposed system. Our observations indicate that predator–prey system is stable without disease but high infection rate drive the predator population toward extinction. We also observe that predation of vulnerable infected prey makes the disease to eradicate into the community composition of the model system. Local stability analysis of the interior equilibrium point near the disease-free equilibrium point is worked out. To study the global dynamics of the system, numerical simulations are performed. Our simulation results show that for higher values of the force of infection in the prey population the predator population goes to extinction. Our numerical analysis reveals that predation rates specially on susceptible prey population and recovery of infective predator play crucial role for preventing the extinction of the susceptible predator and disease propagation.

Time-delayed predator–prey interaction with the benefit of antipredation response in presence of refuge

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Sudeshna Mondal ◽  
Guruprasad Samanta
Keyword(s):  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Prey Population ◽  
Predator Prey ◽  
Terrestrial Vertebrates ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Refuge Area ◽  
Prey Interaction ◽  
Transcritical Bifurcations

AbstractA field experiment on terrestrial vertebrates observes that direct predation on predator–prey interaction can not only affect the population dynamics but the indirect effect of predator’s fear (felt by prey) through chemical and/or vocal cues may also reduce the reproduction of prey and change their life history. In this work, we have described a predator–prey model with Holling type II functional response incorporating prey refuge. Irrespective of being considering either a constant number of prey being refuged or a proportion of the prey population being refuged, a different growth rate and different carrying capacity for the prey population in the refuge area are considered. The total prey population is divided into two subclasses: (i) prey x in the refuge area and (ii) prey y in the predatory area. We have taken the migration of the prey population from refuge area to predatory area. Also, we have considered a benefit from the antipredation response of the prey population y in presence of cost of fear. Feasible equilibrium points of the proposed system are derived, and the dynamical behavior of the system around equilibria is investigated. Birth rate of prey in predatory region has been regarded as bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighborhood of the interior equilibrium point. Moreover, the conditions for occurrence of transcritical bifurcations have been determined. Further, we have incorporated discrete-type gestational delay on the system to make it more realistic. The dynamical behavior of the delayed system is analyzed. Finally, some numerical simulations are given to verify the analytical results.

scholarly journals Dynamics of Predator-Prey Model Interaction with Harvesting Effort

2020 ◽  
Vol 6 (2) ◽  
pp. 93-103
Author(s):  
Muhammad Ikbal ◽  
Riskawati
Keyword(s):  
Response Function ◽  
Equilibrium Points ◽  
Economic Value ◽  
Type I ◽  
Model Interaction ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Predator Model ◽  
The Stability ◽  
Different Response

In this research, we study and construct a dynamic prey-predator model. We include an element of intraspecific competition in both predators. We formulated the Holling type I response function for each predator. We consider all populations to be of economic value so that they can be harvested. We analyze the positive solution, the existence of the equilibrium points, and the stability of the balance points. We obtained the local stability condition by using the Routh-Hurwitz criterion approach. We also simulate the model. This research can be developed with different response function formulations and harvest optimization.

ANALYSIS OF STABILITY AND PERSISTENCE IN A RATIO-DEPENDENT PREDATOR-PREY RESOURCE MODEL

2009 ◽  
Vol 02 (01) ◽  
pp. 107-118 ◽  
Author(s):  
H. I. FREEDMAN ◽  
MANJU AGARWAL ◽  
SAPNA DEVI
Keyword(s):  
Population Density ◽  
Original Model ◽  
Prey Population ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Ratio Dependent ◽  
Analysis Of Stability ◽  
Transformation Of Variables ◽  
Mathematical Analyses

This paper deals with a predator-prey model having ratio-dependent functional response with an additional predator resource. By means of a transformation of variables, we transform the model into a dynamical system in such a way that there is a one-to-one correspondence between the positive values of the original model and positive values of the transformed model, so that the results which are true for the transformed model are also valid for the original model. Mathematical analyses of the model equations with regard to the nature of equilibria, boundedness of solutions, and persistence are carried out. We obtain conditions which influence the boundedness and persistence of all the populations. From numerical calculations, we show that in the absence of any resource, the predator population density decreases and is less than the prey population density, but in the presence of a resource, the predator population density becomes enhanced and dominates the prey population density.

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