ZOO 4400/5400 Population Ecology

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Interspecific competiton -- paired logistic equations
unstable coexistence case

Embedded QuickTime Movie
Click on the image below to start the "movie".  A control bar will appear below the graph; the various buttons will allow you to stop and start it.

Note the curved trajectory -- in this case, though the point jumps extremely quickly down below an isocline (remember, when we are above K, the logistic shows exponential decay).  The it crawls at a decreasing rate toward the Y-axis, and the end result is extinction of N1.

Parameters for this animation:  r1 = r2 = 0.5, K1K2 = 1,000, g12g21 = 1.5.
The high gamma values here are what drive the instability.

Go to animation of stable case with straight trajectory

 Go to animation of stable case with curved trajectory