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Population Model with Competition

Population Model with Competition. Doreen De Leon Math 191T, September 23, 2005. Overview. The model Analysis of stationary points Example. A Population Model of Competition. Stationary Points. Other Stationary Points. Observations.

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Population Model with Competition

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  1. Population Model with Competition Doreen De Leon Math 191T, September 23, 2005

  2. Overview • The model • Analysis of stationary points • Example

  3. A Population Model of Competition

  4. Stationary Points

  5. Other Stationary Points

  6. Observations • The x-coordinate of the first stationary point is positive only if bm > dk • The point (0,0) is only semistable • There is always one stationary point calculated with an x-coordinate less than zeros (which means it is physically impossible).

  7. Type of Stationary Points • We need to find the eigenvalues of the above matrix • Positive (negative) eigenvalues imply unstable (stable) stationary point

  8. The Eigenvalues • We determine the eigenvalues of the matrix L to be:

  9. Implications of Eigenvalues

  10. Example Phase Portrait

  11. Stationary Points

  12. Another Phase Portrait

  13. Stationary Points

  14. Conclusions of the Phase Portratis • For both plots, (0, 2) is a stable node • In the second plot, we also have a stable focus, (3/7, 8/7)

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