Large-scale pattern formation for spikes in reaction-diffusion systems

Many reaction-diffusion systems exhibit patterns consisting of spikes (or spots), and numerous techniques have been developed over the years to study them. In the limit of many spikes, we develop a mean-field theory to describe an effective spike density. The resulting description consists of either a PDE, or an integral equation depending on the system. Of particular interest is the effect of heterogeneities on pattern formation, such as non-uniform feed-rate, or a domain of variable thickness. 

In two dimensions, spots typically form a hexagonal structure. Hexagonal lattice is a special case of a regular lattice generated by vectors of equal length, 30 degrees apart. For Schnakenberg model, we show that any lattice whose angle is between 25.7 and 37.6 degrees, is stable. 

Prof. Theodore Kolokolnikov obtained his PhD from UBC in 2004 under supervision of Michael Ward. His research interests include pattern formation in PDEs, dynamical systems, mathematical modelling, stochastic processes, multi-particle systems and graph theory. He has been at Dalhousie University since 2006. He is the recipient of CAIMS/PIMS Earlier Career Award in Applied Mathematics prize in 2012. He was awarded NSERC Accelearator award in 2014, and Killam Professorship in 2018.