Semi non-standard trimean algorithm for Rosenzweig-MacArthur interaction model

Mohammad Khatim Hasan, Noor Ashikin Othman, Samsul Ariffin Abdul Karim, Jumat Sulaiman

Research output: Contribution to journalArticle

Abstract

Most real world natural systems are shows seasonal behaviour due to seasonal environmental or climate change. As a results, many species display seasonal changes in their life history parameters. It is crucial to comprehend how the seasonal forcing controls the behaviour of the population dynamics. The Rosenzweig-MacArthur model is a system with at least two ordinary differential equations used in population dynamics to model the interaction of predator and prey bonding. Rosenzweig-MacArthur model overcome the weakness of Lotka-Volterra model to simulate interaction between two species. In Rosenzweig-MacArthur model, logistic growth rate of prey is resource limited. The model utilizes Holling type II as the functional response representation. The purpose of the study is to construct method to improve simulation on the behaviour of interactions between species and predicting equilibrium point accurately and fast. Current methods seem to predict accurately the equilibrium point if only small mesh size used. Using small mesh size will require long simulation time to predict the equilibrium point. Able to increase the mesh size will increase the speed of predicting the equilibrium point. In this paper, we propose three new semi non-standard trimean algorithms to simulate the behaviour of interaction between species represented by Rosenzweig-MacArthur model. The new algorithms apply a hybrid of semi non-standard approach and trimean to approximate the nonlinear terms in the differential equation model. Two cases of experiment conducted to examine the performance of all three semi non-standard schemes. Result shows that all three new semi non-standards schemes accurately predict the equilibrium point (0.25, 0.46875) even using big mesh size (h = 4.6 and h = 2.1) for both cases. Thus, all three semi non-standard schemes fulfil the purpose of this study.

Original languageEnglish
Pages (from-to)1520-1527
Number of pages8
JournalInternational Journal on Advanced Science, Engineering and Information Technology
Volume8
Issue number4-2
Publication statusPublished - 1 Jan 2018

Fingerprint

Population Dynamics
Behavior Control
Climate Change
Population dynamics
population dynamics
attachment behavior
Growth
logit analysis
Ordinary differential equations
Climate change
Logistics
life history
climate change
Differential equations
predators
methodology
Object Attachment
Experiments

Keywords

  • Interaction between species
  • Rosenzweig-MacArthur model
  • Semi non-standard discretization
  • Trimean

ASJC Scopus subject areas

  • Computer Science(all)
  • Agricultural and Biological Sciences(all)
  • Engineering(all)

Cite this

Semi non-standard trimean algorithm for Rosenzweig-MacArthur interaction model. / Hasan, Mohammad Khatim; Othman, Noor Ashikin; Karim, Samsul Ariffin Abdul; Sulaiman, Jumat.

In: International Journal on Advanced Science, Engineering and Information Technology, Vol. 8, No. 4-2, 01.01.2018, p. 1520-1527.

Research output: Contribution to journalArticle

Hasan, Mohammad Khatim ; Othman, Noor Ashikin ; Karim, Samsul Ariffin Abdul ; Sulaiman, Jumat. / Semi non-standard trimean algorithm for Rosenzweig-MacArthur interaction model. In: International Journal on Advanced Science, Engineering and Information Technology. 2018 ; Vol. 8, No. 4-2. pp. 1520-1527.
@article{e262ad0a86e649f48582b75f025ef660,
title = "Semi non-standard trimean algorithm for Rosenzweig-MacArthur interaction model",
abstract = "Most real world natural systems are shows seasonal behaviour due to seasonal environmental or climate change. As a results, many species display seasonal changes in their life history parameters. It is crucial to comprehend how the seasonal forcing controls the behaviour of the population dynamics. The Rosenzweig-MacArthur model is a system with at least two ordinary differential equations used in population dynamics to model the interaction of predator and prey bonding. Rosenzweig-MacArthur model overcome the weakness of Lotka-Volterra model to simulate interaction between two species. In Rosenzweig-MacArthur model, logistic growth rate of prey is resource limited. The model utilizes Holling type II as the functional response representation. The purpose of the study is to construct method to improve simulation on the behaviour of interactions between species and predicting equilibrium point accurately and fast. Current methods seem to predict accurately the equilibrium point if only small mesh size used. Using small mesh size will require long simulation time to predict the equilibrium point. Able to increase the mesh size will increase the speed of predicting the equilibrium point. In this paper, we propose three new semi non-standard trimean algorithms to simulate the behaviour of interaction between species represented by Rosenzweig-MacArthur model. The new algorithms apply a hybrid of semi non-standard approach and trimean to approximate the nonlinear terms in the differential equation model. Two cases of experiment conducted to examine the performance of all three semi non-standard schemes. Result shows that all three new semi non-standards schemes accurately predict the equilibrium point (0.25, 0.46875) even using big mesh size (h = 4.6 and h = 2.1) for both cases. Thus, all three semi non-standard schemes fulfil the purpose of this study.",
keywords = "Interaction between species, Rosenzweig-MacArthur model, Semi non-standard discretization, Trimean",
author = "Hasan, {Mohammad Khatim} and Othman, {Noor Ashikin} and Karim, {Samsul Ariffin Abdul} and Jumat Sulaiman",
year = "2018",
month = "1",
day = "1",
language = "English",
volume = "8",
pages = "1520--1527",
journal = "International Journal on Advanced Science, Engineering and Information Technology",
issn = "2088-5334",
publisher = "INSIGHT - Indonesian Society for Knowledge and Human Development",
number = "4-2",

}

TY - JOUR

T1 - Semi non-standard trimean algorithm for Rosenzweig-MacArthur interaction model

AU - Hasan, Mohammad Khatim

AU - Othman, Noor Ashikin

AU - Karim, Samsul Ariffin Abdul

AU - Sulaiman, Jumat

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Most real world natural systems are shows seasonal behaviour due to seasonal environmental or climate change. As a results, many species display seasonal changes in their life history parameters. It is crucial to comprehend how the seasonal forcing controls the behaviour of the population dynamics. The Rosenzweig-MacArthur model is a system with at least two ordinary differential equations used in population dynamics to model the interaction of predator and prey bonding. Rosenzweig-MacArthur model overcome the weakness of Lotka-Volterra model to simulate interaction between two species. In Rosenzweig-MacArthur model, logistic growth rate of prey is resource limited. The model utilizes Holling type II as the functional response representation. The purpose of the study is to construct method to improve simulation on the behaviour of interactions between species and predicting equilibrium point accurately and fast. Current methods seem to predict accurately the equilibrium point if only small mesh size used. Using small mesh size will require long simulation time to predict the equilibrium point. Able to increase the mesh size will increase the speed of predicting the equilibrium point. In this paper, we propose three new semi non-standard trimean algorithms to simulate the behaviour of interaction between species represented by Rosenzweig-MacArthur model. The new algorithms apply a hybrid of semi non-standard approach and trimean to approximate the nonlinear terms in the differential equation model. Two cases of experiment conducted to examine the performance of all three semi non-standard schemes. Result shows that all three new semi non-standards schemes accurately predict the equilibrium point (0.25, 0.46875) even using big mesh size (h = 4.6 and h = 2.1) for both cases. Thus, all three semi non-standard schemes fulfil the purpose of this study.

AB - Most real world natural systems are shows seasonal behaviour due to seasonal environmental or climate change. As a results, many species display seasonal changes in their life history parameters. It is crucial to comprehend how the seasonal forcing controls the behaviour of the population dynamics. The Rosenzweig-MacArthur model is a system with at least two ordinary differential equations used in population dynamics to model the interaction of predator and prey bonding. Rosenzweig-MacArthur model overcome the weakness of Lotka-Volterra model to simulate interaction between two species. In Rosenzweig-MacArthur model, logistic growth rate of prey is resource limited. The model utilizes Holling type II as the functional response representation. The purpose of the study is to construct method to improve simulation on the behaviour of interactions between species and predicting equilibrium point accurately and fast. Current methods seem to predict accurately the equilibrium point if only small mesh size used. Using small mesh size will require long simulation time to predict the equilibrium point. Able to increase the mesh size will increase the speed of predicting the equilibrium point. In this paper, we propose three new semi non-standard trimean algorithms to simulate the behaviour of interaction between species represented by Rosenzweig-MacArthur model. The new algorithms apply a hybrid of semi non-standard approach and trimean to approximate the nonlinear terms in the differential equation model. Two cases of experiment conducted to examine the performance of all three semi non-standard schemes. Result shows that all three new semi non-standards schemes accurately predict the equilibrium point (0.25, 0.46875) even using big mesh size (h = 4.6 and h = 2.1) for both cases. Thus, all three semi non-standard schemes fulfil the purpose of this study.

KW - Interaction between species

KW - Rosenzweig-MacArthur model

KW - Semi non-standard discretization

KW - Trimean

UR - http://www.scopus.com/inward/record.url?scp=85055334928&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055334928&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85055334928

VL - 8

SP - 1520

EP - 1527

JO - International Journal on Advanced Science, Engineering and Information Technology

JF - International Journal on Advanced Science, Engineering and Information Technology

SN - 2088-5334

IS - 4-2

ER -