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REU 2004. Population Models Day 2 Predator Prey. REU’04—Day 2. Today we have 2 species; one predator y(t) (e.g. wolf) and one its prey x(t) (e.g. hare). Actual Data. Model. Want a DE to describe this situation. dx/dt= ax-bxy = x(a-by) dy/dt=-cx+dxy = y(-c+dx). 3.
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REU 2004 Population Models Day 2Predator Prey
REU’04—Day 2 • Today we have 2 species; one predator y(t) (e.g. wolf) and one its prey x(t) (e.g. hare)
Model • Want a DE to describe this situation • dx/dt= ax-bxy = x(a-by) dy/dt=-cx+dxy = y(-c+dx) 3 • Could get rid of __________constants
Called Lotka-Volterra Equation, Lotka & Volterra independently studied this post WW I. • Fixed points: (0,0), (c/d,a/b)
What are you going to do? • Try to use analysis to argue that this is indeed the phase portrait.
OK what now? • 3 species food chain! • x = worms; y= robins; z= eagles dx/dt = ax-bxydy/dt= -cy+dxy-eyzdz/dt= -fz+gyz
New tools • Invariant sets & trapping regions!