Phase Plane Analysis: Worked Example | Rabbits Vs. Sheep Species Competition, Population Biology

[@kylejohnson8447]

This playlist is such a huge help. Thanks so much

[@ProfessorRoss]

You're so welcome! Thanks for watching Kyle.

[@學習中的哈密瓜]

Why is the trajectories will approach the slow eigendirections? 9:38

[@ProfessorRoss]

Because of the (relatively) fast eigendirections. The speed of motion in phase space in the directions normal to the slow eigendirections are exponentially faster, giving that appearance of convergence onto the lower dimensional 'slow manifold'. I hope that helps. Thanks for watching!

[@bileti99]

Thank you!

[@youyoubrink7425]

Why isn't point 1,1 a spiral point? Because the eigenvalues are -1+/-sqrt(2)i no?

[@ProfessorRoss]

The eigenvalues are only real, it's -1+/-sqrt(2). So one is real and positive and the other real and negative, making this a saddle point.

[@alb2935]

Great!