1 / 10

REU 2004

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.

gillian-livingston
Download Presentation

REU 2004

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. REU 2004 Population Models Day 2Predator Prey

  2. 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)

  3. Actual Data

  4. 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

  5. Called Lotka-Volterra Equation, Lotka & Volterra independently studied this post WW I. • Fixed points: (0,0), (c/d,a/b)

  6. The ANSWER:

  7. Solution vs time

  8. What are you going to do? • Try to use analysis to argue that this is indeed the phase portrait.

  9. OK what now? • 3 species food chain! • x = worms; y= robins; z= eagles dx/dt = ax-bxydy/dt= -cy+dxy-eyzdz/dt= -fz+gyz

  10. New tools • Invariant sets & trapping regions!

More Related