On “small” data blow-up in a three species food chain model

Abstract

In Parshad et al. (2015) we showed that both the ODE and PDE versions of a classical three species food chain model, possess solutions that blow-up in finite time, for sufficiently large initial data. The object of the current work is to show that solutions to the PDE model can blow-up in finite time for small initial data as well. To the best of our knowledge, this is the first example of “diffusion induced” blow-up phenomenon for small initial data, in a three species system, where the corresponding ODE also has a possibility to blow-up for large initial data.