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March 14, 2013

Speaker: Mitchell Kovacic, Ontario Tech University

Title: Matrix-Free Pseudo-Arclength Continuation On A Recent, Dynamically Rich Animal Aggregation Model

Abstract: First a brief overview of animal aggregation models is given, explaining what they are and their different ‘flavours’. A relatively new nonlocal animal aggregation model is introduced which exhibits a zoo of interesting dynamics. Several examples of the dynamics possible are showcased along with an example where bifurcations in the system lead to realistically observable dynamics. A short description of bifurcations and continuation methods is given along with reasoning for the use of continuation methods for observing dynamics in the system. Pseudo-spectral methods are introduced and lightly touched on, highlighting nontrivial applications of the methods in the model with examples where it may cause problems. A recently developed algorithm for a matrix-free pseudo-arclength continuation method is shown with emphasis on the advantages over conventional continuation methods. Finally the Generalized Minimal Residual (GMRES) method is introduced for the solving of systems arising from the pseudo-arclength continuation. Current results are then given with highlight to future use of continuation software being developed.