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

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 alpha. The results show that the stability indices vary from +infinity down to positive values as alpha increases. Biologically, +infinity 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 alpha. The patterns show that for a low alpha , the sea turtles will survive in the next 10 years while when alpha 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.