Reaction diffusion systems for living on an isolated Island

This work investigates the distribution of population in an isolated region, i.e. Easter Island, and the interaction between settlers and resources. The temporal differential system is employed to model the hypothesis that the misuse of resources in Easter Island can cause people extinct. The local analysis of this system is revised. Then, we extend the temporal system by adding more realistic diffusion terms, which presents the spatial distribution of the population in the Island. The spatio-temporal system is analysed in one and two spatial dimensions with a diagonal diffusion matrix. Travelling wave solutions of the spatio-temporal system appear in different profiles, namely, front, pulse and chaotic ones. The attained results reveal that the people misused the resources in Easter Island may cause extinction also in one spatial dimension. For two spatial dimensions, the driven instability is discussed to examine the existence of Turing patterns.