I'm going through these videos to get a grasp of the techniques we use in my superconducting electronics course, since the nonlinear dynamics course in my uni was cut some 10 years ago. It is a real delight how well it is presented, it's really easy to scrible along with it.
I was initially bit confused about the three fixed points (roots 0, A, K) for the population dynamics with Allee effect, instead of only two roots for the quadratic equation. That is because I was thinking of including the Allee effect by shifting the function by A, that is from dN/dt = r N (1 - N/K) to dN/dt = r (N-A) (1 - (N-A)/K). In that case N = 0 can not be a fixed point. But it turns out that inclusion of Allee effect is done by a cubic equation with an additional term as dN/dt = r N (N/A - 1) (1 - N/K), where all three fixed points make sense. More here en.wikipedia.org/wiki/Allee_effect . Thank you very much for the beautiful lectures Dr. Shane Ross.
I'm going through these videos to get a grasp of the techniques we use in my superconducting electronics course, since the nonlinear dynamics course in my uni was cut some 10 years ago. It is a real delight how well it is presented, it's really easy to scrible along with it.
Thank you so much! I'm glad it's helping.
I was initially bit confused about the three fixed points (roots 0, A, K) for the population dynamics with Allee effect, instead of only two roots for the quadratic equation. That is because I was thinking of including the Allee effect by shifting the function by A, that is from dN/dt = r N (1 - N/K) to dN/dt = r (N-A) (1 - (N-A)/K). In that case N = 0 can not be a fixed point.
But it turns out that inclusion of Allee effect is done by a cubic equation with an additional term as dN/dt = r N (N/A - 1) (1 - N/K), where all three fixed points make sense. More here en.wikipedia.org/wiki/Allee_effect .
Thank you very much for the beautiful lectures Dr. Shane Ross.
Thank you so much. I'm glad you appreciate the lectures.
Thank you so much!!!!!
You're welcome!