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September 30, 2009

Speaker: Dr. Raluca Eftimie, Department of Mathematics and Statistics, McMaster University

Title: Pattern formation in a nonlocal hyperbolic model animal aggregations

Abstract: We investigate the formation and movement of self-organizing collectives of animals in homogeneous environments. In this context, we present a general modeling framework that incorporates how individuals perceive information from neighbours, and the amount of information perceived. In particular, we construct a one-dimensional nonlocal hyperbolic model which assumes that the interactions with neighbours (that is, attraction towards individuals that are far away, repulsion from those that are nearby, and alignment with individuals at intermediate distances) are determined by the information perceived. This model generates at least 13 spatial and spatiotemporal patterns. Some of these patterns are classical, such as stationary pulses, travelling pulses, or travelling trains. However, the majority of these patterns are novel, such as the patterns we call zigzag pulses and feathers. This modeling framework presents a unitary approach for the investigation of animal group formation and movement, since all the patterns obtained with other parabolic and hyperbolic models existent in the literature can be understood in terms of a single model operating in different parameter regimes, represented by different communication mechanisms. 

Disciplines: Biology, Mathematics