Characterization of Basin of Attraction for an Attractor in a Discrete Prey-Predator Sea Turtle-Human Interaction Model using Stability Index Approach

Mohd Tirmizi  Mohd Lutfi; Ummu Atiqah Mohd Roslan; Fatemeh Helen  Ghane; Ahmad Fadillah  Embong

doi:10.11113/mjfas.v18n4.2622

Authors

Mohd Tirmizi Mohd Lutfi Special Interest Group on Modelling and Data Analytics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia
Ummu Atiqah Mohd Roslan Special Interest Group on Modelling and Data Analytics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia
Fatemeh Helen Ghane Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, P.O. Box 1159-91775, Iran
Ahmad Fadillah Embong Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia

DOI:

https://doi.org/10.11113/mjfas.v18n4.2622

Keywords:

Dynamical systems, attractor, riddled basin, stability index, sea turtle-human model

Abstract

Drastic declines of the number of sea turtles have become a global issue since decades ago. This is due to overexploitation through human activities in various ways, such as poaching and trapping in the fishing nets, consuming their eggs and meat, other than being threatened by pollution, habitat destruction and many more. Therefore, it is our interest to investigate this issue through mathematical modelling. For that purpose, a discrete model of interaction between sea turtles and humans is proposed in this paper. The objective of this paper is to determine sustainability of sea turtle population in the future. In order to achieve this, an approach called the stability index, has been implemented on the basin of attraction of an attractor in the model proposed for different values of consumption rate The results show that the stability indices vary from down to positive values as increases. Biologically, index means that the sea turtles will survive, while positive index means that riddled basin has occurred in which it is predicted that the sea turtles might extinct or not depending on the initial population existing in a habitat. Moreover, the time series have also been plotted for different values of The patterns show that for a low the sea turtles will survive in the next 10 years while when is high, the sea turtle will extinct in less than two years. Thus, the results of this model could significantly be used to urge humans to stop exploiting these unique creatures and start appreciating their existence in the ecosystem.

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