Alladi Ramakrishnan Hall

Effect of non-local interactions in a prey-predator system

Moitri Sen

Department of Mathematics, National Institute of Technology (NIT) Patna

The idea of `Pattern formation' first came into the picture with the seminal work of Turing in the year 1952. Patterns are mainly classified into two types, namely,Turing patterns and non-Turing patterns. Turing patterns, known as cold spots,hot spots, labyrinthine, mixture of spots and stripes etc. Non-Turing patterns can be divided into periodic(traveling waves, periodic traveling waves, spiral and target patterns) and aperiodic (interacting spiral chaos and spatio-temporal chaos) in time. A typical presumption of modelling the spatio-temporal prey-predator system is that the interaction between the species is taking place over a local scale. But in reality due to intra-specific competition, inter-specific
competition, predation etc. related with the evolutionary changes several species are affected by non-local interactions. In this talk I will mainly talk about a spatio-temporal prey-predator model with non-local interaction
terms where the functional response is ratio dependent and the predator death rate is density dependent. Non-local interactions are considered for prey and predator species to describe the non-local intra-specific competition for limited resources. We show that the region of pattern formation increases with the increase of the range of non-local interaction.