Alladi Ramakrishnan Hall

The shaping role of non-local interactions in formation of spatio-temporal patterns

Mrinal Kanti Pal

Department of Applied Mathematics, Calcutta University

Majority of the reaction-diffusion systems that arise in different physical and biological scenarios only take into account local space or time variables, leaving out any potential spatial dependence on nearby points or conceivable memory effects. Researchers have created non-local models using convolution integrals to get around this limitation. These models take into account how the system’s temporal evolution depends on spatial points scattered across the area and on earlier periods also. In contrast to its local counterpart, the non-local reaction diffusion system is able to produce more accurate spatio-temporal patterns that are in good agreement with field data. To that end, this talk will take into account two crucial ecological contexts, the pelagic ecosystem and the dry-land ecosystem, in which a significant number of reaction-diffusion models have been proposed over time to model the phenomenon of spatial pattern formation. I have incorporated non-local interactions into these models and compared the local reaction-diffusion models under consideration with their non-local modifications using standard techniques of dynamical systems.