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Yuni Yulida
Program Studi Matematika FMIPA Universitas Lambung Mangkurat
Agriculture, Biological Sciences & Forestry Arts Humanities Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Energy Engineering Materials Science & Nanotechnology Mathematics Mechanical Engineering Medicine & Pharmacology Physics Social Sciences Transportation Other

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Journal : Desimal: Jurnal Matematika

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Analysis of stability and bifurcation in logistics models with harvesting in the form of the holling type III functional response Yuni Yulida; Firman Nurrobi; Faisal Faisal; Muhammad Ahsar Karim
Desimal: Jurnal Matematika Vol 5, No 1 (2022): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (403.496 KB) | DOI: 10.24042/djm.v5i1.11828

Abstract

The logistic model can be applied in the field of biological studies to investigate population growth problems and some important aspects of the ecological situation. This model is a growth model with a limited population growth rate, and ecologists describe this rate as carrying capacity. Carrying capacity can be interpreted as the ideal population size, where individuals in the population can live properly in their environment. The growth rate of a population can be influenced by the harvesting factor, in this case, it is assumed that harvesting is not constant. The effect of the harvest on the growth rate can be analyzed mathematically by using the Holling type III functional response. In this paper, describe the formation of a logistic model taking into account the effects of harvesting, using the Holling type III functional response. Then,  perform a nondimensional process in the model, namely simplifying a model that has four parameters to a model that only has two parameters. Next, determine the equilibrium point of the model, perform a stability analysis at that equilibrium point, and investigate the possibility of bifurcation. As result, first obtained a logistic model which has two non-dimensional parameters, where one of the equilibrium points is zero and is unstable. Next, determine another equilibrium point through an implicit equation and investigate its stability through simulation. Finally, obtained two equilibrium points, which are fold bifurcation.
Co-Authors Aji Wiratama Akhmad Yusuf Alya Hanifah Arif Ana Rizki Mahmudah Andi Tri Wardana Annisa Rahayu Arie Wijaya Audinta Sakti Firmansyah Azkia Khairal Jamil Azkia Khairal Jamil Azkia Khairal Jamil Bizaini Bizaini DEWI ANGGRAINI Dewi Sri Susanti Edy Sarwo Agus Wibowo Faisal Faisal Faisal Faisal Faisal Faisal Farohatin Na'imah Firman Nurrobi Fitri Nor Annisa Fitriani Fitriani Friska Erlina Gabriel Henokh Gultom Gian Septiansyah Gian Septiansyah Gusti Muhammad Rosyadi Haidir Ahsana Helfa Oktafia Afisha Herlyn Basrina Lestia, Aprida Siska Miftahul Jannah Miftahul Jannah Muhammad Afief Balya Muhammad Ahsar Karim Muhammad Ahsar Karim Muhammad Ahsar Karim Muhammad Mahfuzh Shiddiq Muhammad Mahfuzh Shiddiq Mursyidah Pratiwi Mustika Khadijah Na'imah Hijriati Noor Fakhriani Nor Hidayati Nurul huda Pardi Affandi Rahayu, Annisa Rahmi Hidayati Raihan Nooriman Rezky Putri Rahayu Riska Fitria Riska Fitria Rizky Purnama Wulandari Sinar Ismaya Sofia Faridatun Nisa Thresye Thresye Tri Puspa Lestari Vika Astuti Wuri Setyana Sari Yogi Apriyanto