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Ontario Tech acknowledges the lands and people of the Mississaugas of Scugog Island First Nation.

We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

Learn more about Indigenous Education and Cultural Services

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