International Journal on Advanced Science, Engineering and Information Technology, Vol. 8 (2018) No. 4-2: Special Issue on Empowering the Nation via 4IR (The Fourth Industrial Revolution)., pages: 1520-1527, Chief Editor: Khairuddin Omar | Editorial Boards : Shahnorbanun Sahran Hassan, Nor Samsiah Sani, Heuiseok Lim & Danial Hoosyar, DOI:10.18517/ijaseit.8.4-2.6779

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

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

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.

Keywords:

semi non-standard discretization, trimean, Rosenzweig-MacArthur model, interaction between species.

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