Harvesting and Hopf Bifurcation in a Prey-Predator Model with Holling Type IV Functional Response

Agarwal, Manju; Pathak, Rachana

doi:10.26708/ijmsc.2012.1.2.12

Cited by 21 publications

(12 citation statements)

References 10 publications

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“…Penelitian ini didasari bahwa interaksi predator-prey tidak selamanya monoton, yaitu saat dimana populasi mangsa meningkat maka populasi pemangsa akan menurun, dikarenakan adanya sifat bertahan atau defending dari mangsa. Berikut persamaan fungsi respon Monod-Haldane [6]:…”

Section: Pendahuluanunclassified

Analisis Kestabilan Model Interaksi Predator-Prey Dengan Fungsi Respon Monod-Haldane Dan Perilaku Anti Pemangsa

Gaib

Ja’a

2020

Euler J. Ilm. Mat. Sains dan Teknol.

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This article examines a competing prey-predator model using the Monod-Haldane response function and anti-predator behavior. This article discusses equilibrium point determination, equilibrium point stability analysis, and numerical simulation. Obtained three equilibrium points, namely T1, T2, and T3, where the equilibrium-point is always saddle, the stability of the equilibrium points T2 and T3 will be stable if it meets the predetermined parameter requirements. There are two cases in the equilibrium point where the first case is vertically stable and the second case is spiral stable.

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Section: Pendahuluanunclassified

Analisis Kestabilan Model Interaksi Predator-Prey Dengan Fungsi Respon Monod-Haldane Dan Perilaku Anti Pemangsa

Gaib

Ja’a

2020

Euler J. Ilm. Mat. Sains dan Teknol.

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“…In recent years, one of the important predatorprey models with the functional response is the Holling type -IV, originally due to Holling which has been extensively studies in many articles [4][5][6]11].Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. There has been growing interest in the study of prey-predator discrete time models described by differential equations.…”

Section: Iintroductionmentioning

confidence: 99%

“…Two species models like Holling type II, III and IV of predator to its prey have been extensively discussed in the literature [2][3][4][5][6]9,16]. Leslie-Gower predator-prey model with variable delays, bifurcation analysis with time delay, global stability in a delayed diffusive system has been studied [8,12,14].…”

Section: Iintroductionmentioning

confidence: 99%

Typical Measures on Discrete Time Prey-Predator Model with HarvestedPrey

Lakshmi¹,

Gunasekaran²,

Vijaya³

2014

IJCOA

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Prey-predator model has received much attention during the last few decades due to its wide range of applications. There are many different kinds of prey-predator models in mathematical ecology. The discrete time models governed by difference equations are more appropriate than the continuous time models to describe the prey-predator relations. Thispaper aims to study the effect of harvested prey species on a Holling type IV prey predator model involving intra-specific competition. Harvesting has a strong impact on the dynamic evolution of a population. This model represents mathematically by nonlinear differential equations. The locally asymptotic stability conditions of all possible equilibrium points were obtained. The stability/instability of nonnegative equilibrium and associated bifurcation were investigated by analysing the characteristic equations. Moreover, bifurcation diagram were obtained for different values of parameters of proposed model. Finally, numerical simulation was used to study the global and rich dynamics of that model.

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“…Ruan and Xiao 2001;Saeez and Gonzalez-Olivares 1999;Skalski and Gilliam 2001;Akcakaya et al 1995;Wang et al 2007) are used among which Holling type II, III and IV are the extensively used in literature of mathematical biology (cf. Aziz-Alaoui and Okiye 2003;Camara and Alaoui 2008;Mukherjee et al 2011;Lu and Wang 2011;Zhang et al 2008;Agarwal and Pathak 2012;Chen et al 2013;Zhen and Zhong 2013). The effects of the presence of additional food in the ecological system is taken into account through the modification of functional response term (cf.…”

Section: Introductionmentioning

confidence: 99%

Effects of intraspecific competition of prey in the dynamics of a food chain model

Shome

Maiti²,

Poria

2016

Model. Earth Syst. Environ.

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In this paper, dynamical behavior of simple prey-predator model with Holling type II functional response involving additional food for predator along with intraspecific competition of prey is proposed and analyzed. The stability criteria of solutions are investigated by varying quantity and quality of additional food and intraspecific competition of prey population. Conditions for Hopf bifurcation are derived analytically. Numerical simulation results are presented to observe the time evolution of the system. This study may be useful to understand the effects of intraspecific competition in real world ecological systems.

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Harvesting and Hopf Bifurcation in a Prey-Predator Model with Holling Type IV Functional Response

Cited by 21 publications

References 10 publications

Analisis Kestabilan Model Interaksi Predator-Prey Dengan Fungsi Respon Monod-Haldane Dan Perilaku Anti Pemangsa

Analisis Kestabilan Model Interaksi Predator-Prey Dengan Fungsi Respon Monod-Haldane Dan Perilaku Anti Pemangsa

Typical Measures on Discrete Time Prey-Predator Model with HarvestedPrey

Effects of intraspecific competition of prey in the dynamics of a food chain model

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