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Semi Non-Standard Trimean Algorithm for Rosenzweig-MacArthur Interaction Model

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@article{IJASEIT6779,
   author = {Mohammad Khatim Hasan and Noor Ashikin Othman and Samsul Ariffin Abdul Karim and Jumat Sulaiman},
   title = {Semi Non-Standard Trimean Algorithm for Rosenzweig-MacArthur Interaction Model},
   journal = {International Journal on Advanced Science, Engineering and Information Technology},
   volume = {8},
   number = {4-2},
   year = {2018},
   pages = {1520--1527},
   keywords = {semi non-standard discretization, trimean, Rosenzweig-MacArthur model, interaction between species.},
   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 ( and ) for both cases. Thus, all three semi non-standard schemes fulfil the purpose of this study.},
   issn = {2088-5334},
   publisher = {INSIGHT - Indonesian Society for Knowledge and Human Development},
   url = {http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=6779},
   doi = {10.18517/ijaseit.8.4-2.6779}
}

EndNote

%A Hasan, Mohammad Khatim
%A Othman, Noor Ashikin
%A Abdul Karim, Samsul Ariffin
%A Sulaiman, Jumat
%D 2018
%T Semi Non-Standard Trimean Algorithm for Rosenzweig-MacArthur Interaction Model
%B 2018
%9 semi non-standard discretization, trimean, Rosenzweig-MacArthur model, interaction between species.
%! Semi Non-Standard Trimean Algorithm for Rosenzweig-MacArthur Interaction Model
%K semi non-standard discretization, trimean, Rosenzweig-MacArthur model, interaction between species.
%X 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 ( and ) for both cases. Thus, all three semi non-standard schemes fulfil the purpose of this study.
%U http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=6779
%R doi:10.18517/ijaseit.8.4-2.6779
%J International Journal on Advanced Science, Engineering and Information Technology
%V 8
%N 4-2
%@ 2088-5334

IEEE

Mohammad Khatim Hasan,Noor Ashikin Othman,Samsul Ariffin Abdul Karim and Jumat Sulaiman,"Semi Non-Standard Trimean Algorithm for Rosenzweig-MacArthur Interaction Model," International Journal on Advanced Science, Engineering and Information Technology, vol. 8, no. 4-2, pp. 1520-1527, 2018. [Online]. Available: http://dx.doi.org/10.18517/ijaseit.8.4-2.6779.

RefMan/ProCite (RIS)

TY  - JOUR
AU  - Hasan, Mohammad Khatim
AU  - Othman, Noor Ashikin
AU  - Abdul Karim, Samsul Ariffin
AU  - Sulaiman, Jumat
PY  - 2018
TI  - Semi Non-Standard Trimean Algorithm for Rosenzweig-MacArthur Interaction Model
JF  - International Journal on Advanced Science, Engineering and Information Technology; Vol. 8 (2018) No. 4-2
Y2  - 2018
SP  - 1520
EP  - 1527
SN  - 2088-5334
PB  - INSIGHT - Indonesian Society for Knowledge and Human Development
KW  - semi non-standard discretization, trimean, Rosenzweig-MacArthur model, interaction between species.
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 ( and ) for both cases. Thus, all three semi non-standard schemes fulfil the purpose of this study.
UR  - http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=6779
DO  - 10.18517/ijaseit.8.4-2.6779

RefWorks

RT Journal Article
ID 6779
A1 Hasan, Mohammad Khatim
A1 Othman, Noor Ashikin
A1 Abdul Karim, Samsul Ariffin
A1 Sulaiman, Jumat
T1 Semi Non-Standard Trimean Algorithm for Rosenzweig-MacArthur Interaction Model
JF International Journal on Advanced Science, Engineering and Information Technology
VO 8
IS 4-2
YR 2018
SP 1520
OP 1527
SN 2088-5334
PB INSIGHT - Indonesian Society for Knowledge and Human Development
K1 semi non-standard discretization, trimean, Rosenzweig-MacArthur model, interaction between species.
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 ( and ) for both cases. Thus, all three semi non-standard schemes fulfil the purpose of this study.
LK http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=6779
DO  - 10.18517/ijaseit.8.4-2.6779