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Comparative analysis of Euler and Runge-Kutta Fehlberg Methods in solving the Lotka-Volterra competitive model/ Nur Hidayah Abd Rahaman ... [et al.]

This study addresses the problem of determining equilibrium and stability in ecosystems where species compete for the same resources, as outlined by the principle of competitive exclusion. It is often challenging to ascertain the rate at which exclusion happens and whether species can coexist in com...

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Main Authors: Abd Rahaman, Nur Hidayah, Ahmad Bakhtiar, Nurizatul Syarfinas, Hajimia, Hafizah, Fauzi, Nur Fatihah, Khairudin, Nur Izzati
Format: Article
Language:English
Published: Universiti Teknologi MARA, Perak 2024
Subjects:
QA Mathematics
Electronic Computers. Computer Science
Online Access:https://ir.uitm.edu.my/id/eprint/106661/1/106661.pdf
https://ir.uitm.edu.my/id/eprint/106661/
http://www.mijuitmjournal.com
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spelling my.uitm.ir.1066612024-11-20T16:51:15Z https://ir.uitm.edu.my/id/eprint/106661/ Comparative analysis of Euler and Runge-Kutta Fehlberg Methods in solving the Lotka-Volterra competitive model/ Nur Hidayah Abd Rahaman ... [et al.] msij Abd Rahaman, Nur Hidayah Ahmad Bakhtiar, Nurizatul Syarfinas Hajimia, Hafizah Fauzi, Nur Fatihah Khairudin, Nur Izzati QA Mathematics Electronic Computers. Computer Science This study addresses the problem of determining equilibrium and stability in ecosystems where species compete for the same resources, as outlined by the principle of competitive exclusion. It is often challenging to ascertain the rate at which exclusion happens and whether species can coexist in competitive environments. To discover these issues, the study investigates the competitive interactions between lions (Panthera Leo) and leopards (Panthera pardus) in the Sabi Sand Game Reserve, South Africa, focusing on whether the dominant competitor, lions, limit the population and distribution of leopards. Using the Lotka-Volterra Competitive model, the research compares numerical solutions obtained through Euler and Runge-Kutta Fehlberg (RKF) methods. It also examines how carrying capacity and initial conditions influence equilibrium and stability in this competition. Data on dietary overlaps between lions and leopards were used to test their competitive dynamics, with lions targeting larger prey and leopards focusing on smaller prey. The findings indicate that the RKF method provides more accurate approximations than Euler's method, with leopards showing a higher carrying capacity and greater resilience in the face of competition from lions. This indicates that leopard populations are less affected by lion presence. The study emphasizes the role of carrying capacity in species survival during competition and highlights the utility of numerical methods for predicting competition outcomes without extended experimentation. These findings contribute to wildlife management strategies, particularly in efforts to restore large carnivores in ecosystems, and improve understanding of competitive exclusion in ecological systems. Universiti Teknologi MARA, Perak 2024-11 Article PeerReviewed text en https://ir.uitm.edu.my/id/eprint/106661/1/106661.pdf Comparative analysis of Euler and Runge-Kutta Fehlberg Methods in solving the Lotka-Volterra competitive model/ Nur Hidayah Abd Rahaman ... [et al.]. (2024) Mathematical Sciences and Informatics Journal (MIJ) <https://ir.uitm.edu.my/view/publication/Mathematical_Sciences_and_Informatics_Journal_=28MIJ=29/>, 5 (2). pp. 95-104. ISSN 2735-0703 http://www.mijuitmjournal.com 10.24191/mij.v5i2.1199 10.24191/mij.v5i2.1199 10.24191/mij.v5i2.1199
institution Universiti Teknologi Mara
building Tun Abdul Razak Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Mara
content_source UiTM Institutional Repository
url_provider http://ir.uitm.edu.my/
language English
topic QA Mathematics
Electronic Computers. Computer Science
spellingShingle QA Mathematics
Electronic Computers. Computer Science
Abd Rahaman, Nur Hidayah
Ahmad Bakhtiar, Nurizatul Syarfinas
Hajimia, Hafizah
Fauzi, Nur Fatihah
Khairudin, Nur Izzati
Comparative analysis of Euler and Runge-Kutta Fehlberg Methods in solving the Lotka-Volterra competitive model/ Nur Hidayah Abd Rahaman ... [et al.]
description This study addresses the problem of determining equilibrium and stability in ecosystems where species compete for the same resources, as outlined by the principle of competitive exclusion. It is often challenging to ascertain the rate at which exclusion happens and whether species can coexist in competitive environments. To discover these issues, the study investigates the competitive interactions between lions (Panthera Leo) and leopards (Panthera pardus) in the Sabi Sand Game Reserve, South Africa, focusing on whether the dominant competitor, lions, limit the population and distribution of leopards. Using the Lotka-Volterra Competitive model, the research compares numerical solutions obtained through Euler and Runge-Kutta Fehlberg (RKF) methods. It also examines how carrying capacity and initial conditions influence equilibrium and stability in this competition. Data on dietary overlaps between lions and leopards were used to test their competitive dynamics, with lions targeting larger prey and leopards focusing on smaller prey. The findings indicate that the RKF method provides more accurate approximations than Euler's method, with leopards showing a higher carrying capacity and greater resilience in the face of competition from lions. This indicates that leopard populations are less affected by lion presence. The study emphasizes the role of carrying capacity in species survival during competition and highlights the utility of numerical methods for predicting competition outcomes without extended experimentation. These findings contribute to wildlife management strategies, particularly in efforts to restore large carnivores in ecosystems, and improve understanding of competitive exclusion in ecological systems.
format Article
author Abd Rahaman, Nur Hidayah
Ahmad Bakhtiar, Nurizatul Syarfinas
Hajimia, Hafizah
Fauzi, Nur Fatihah
Khairudin, Nur Izzati
author_facet Abd Rahaman, Nur Hidayah
Ahmad Bakhtiar, Nurizatul Syarfinas
Hajimia, Hafizah
Fauzi, Nur Fatihah
Khairudin, Nur Izzati
author_sort Abd Rahaman, Nur Hidayah
title Comparative analysis of Euler and Runge-Kutta Fehlberg Methods in solving the Lotka-Volterra competitive model/ Nur Hidayah Abd Rahaman ... [et al.]
title_short Comparative analysis of Euler and Runge-Kutta Fehlberg Methods in solving the Lotka-Volterra competitive model/ Nur Hidayah Abd Rahaman ... [et al.]
title_full Comparative analysis of Euler and Runge-Kutta Fehlberg Methods in solving the Lotka-Volterra competitive model/ Nur Hidayah Abd Rahaman ... [et al.]
title_fullStr Comparative analysis of Euler and Runge-Kutta Fehlberg Methods in solving the Lotka-Volterra competitive model/ Nur Hidayah Abd Rahaman ... [et al.]
title_full_unstemmed Comparative analysis of Euler and Runge-Kutta Fehlberg Methods in solving the Lotka-Volterra competitive model/ Nur Hidayah Abd Rahaman ... [et al.]
title_sort comparative analysis of euler and runge-kutta fehlberg methods in solving the lotka-volterra competitive model/ nur hidayah abd rahaman ... [et al.]
publisher Universiti Teknologi MARA, Perak
publishDate 2024
url https://ir.uitm.edu.my/id/eprint/106661/1/106661.pdf
https://ir.uitm.edu.my/id/eprint/106661/
http://www.mijuitmjournal.com
_version_ 1817847231878791168
score 13.223943

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