Leslie-Gower predator-prey model with stage-structure, Beddington-DeAngelis functional response, and anti-predator behavior

This article discusses the one-prey, one-predator, and the super predator model with different types of functional response. The rate of prey consumption by the predator follows Holling type I functional response and the rate of predator consumption by the super predator follows Holling type II functional response. We identify the existence and stability of critical points and obtain that the extinction of all population points is always unstable, and the other two are conditionally stable i.e., the super predator extinction point and the co-existence point. Furthermore, we give the numerical simulations to describe the bifurcation diagram and phase portraits of the model. The bifurcation diagram is obtained by varying the parameter of the conversion rate of predator biomass into a new super-predator which gives forward and Hopf bifurcation. The forward bifurcation occurs around the super predator extinction point while Hopf bifurcation occurs around the interior of the model. Based on the terms of existence and numerical simulation, we confirm that the conversion rate of predator biomass into a new super-predator controls the dynamics of the system and maintains the existence of predator.

Section: Pendahuluanunclassified

Bifurkasi Hopf pada model prey-predator-super predator dengan fungsi respon yang berbeda

Savitri

Panigoro

2020

“…Due to the stage-structure for interaction between prey and predator, Beay and Saija [5], Beay et al [6], and Moustafa et al [7] studied the dynamics behavior by using Rosenzweig-MacArthur model. Additionally, the dynamics of the stage-structure Leslie-Gower model studied by Lin et al [8], Pratiwi et al [9], Beay and Saija [10], Meng et al [11], and Salamah et al [12].…”

Section: Introductionmentioning

confidence: 99%

A Stage-structure Leslie-Gower Model with Linear Harvesting and Disease in Predator

Beay,

Leleury,

Rijoly

et al. 2023

The growth dynamics of various species are affected by various aspects. Harvesting interventions and the spread of disease in species are two important aspects that affect population dynamics and it can be studied. In this work, we consider a stage-structure Leslie–Gower model with linear harvesting on the both prey and predator. Additionally, we also consider the infection aspect in the predator population. The population is divided into four subpopulations: immature prey, mature prey, susceptible predator, and infected predator. We analyze the existences and stabilities of feasible equilibrium points. Our results shown that the harvesting in prey and the disease in predator impacts the behavioral of system. The situation in the system is more complex due to disease in the predator population. Some numerical simulations are given to confirm our results.

“…Meanwhile, it is known that the condition of existence for E 3 is ν > µ. Thus, we have a [3] 12 > 0 and a [3] 21 > 0. Moreover, we get that a…”

mentioning

confidence: 95%

“…Since Lotka (1925) and Volterra (1931) proposed the predator-prey model known as the Lotka-Volterra model, the mathematical modeling of the ecological model has progressed rapidly. This model is the forerunner of other predator-prey model, such as Leslie-Gower model [1][2][3][4][5] and Rosenzweig-MacArthur model [6][7][8][9]. The dynamic behavior of predator-prey model can be influenced by many factors, such as mortality rates, competition between species, fear of prey, infectious disease, and environment conditions.…”

Section: Introductionmentioning

confidence: 99%

Dynamics in two competing predators-one prey system with two types of Holling and fear effect

Firdiansyah¹,

Nurhidayati²

2021

In this article, it is formulated a predator-prey model of two predators consuming a single limited prey resource. On the other hand, two predators have to compete with each other for survival. The predation function for two predators is assumed to be different where one predator uses Holling type I while the other uses Holling type II. It is also assumed that the fear effect is considered in this model as indirect influence evoked by both predators. Non-negativity and boundedness is written to show the biological justification of the model. Here, it is found that the model has five equilibrium points existed under certain condition. We also perform the local stability analysis on the equilibrium points with three equilibrium points are stable under certain conditions and two equilibrium points are unstable. Hopf bifurcation is obtained by choosing the consumption rate of the second predator as the bifurcation parameter. In the last part, several numerical solutions are given to support the analysis results.