Mathematical Biology. 23: Poincare-Bendixson

UCI Math 113B: Intro to Mathematical Modeling in Biology (Fall 2014)
Lec 23. Intro to Mathematical Modeling in Biology: Poincare-Bendixson
Instructor: German A. Enciso, Ph.D.

Textbook: Mathematical Models in Biology by Leah Edelstein-Keshet, SIAM, 2005

License: Creative Commons CC-BY-SA

Description: UCI Math 113B is intended for both mathematics and biology undergrads with a basic mathematics background, and it consists of an introduction to modeling biological problems using continuous ODE methods (rather than discrete methods as used in 113A). We describe the basic qualitative behavior of dynamical systems in the context of a simple population model. As time allows, we will then discuss other types of models such as chemical reactions inside the cell, or excitable systems leading to oscillations and neuronal signals. The necessary linear algebra is also discussed to avoid including additional requirements for this course.

Recorded on March 5, 2014

[ontheway]

Is the function c1 instead of c2 ? Because for uniqueness of an initial value problem f has to be continuous and del(f)/del(x) has to be continuous.

[deyomash]

I don't get it, we have shown that LV has periodic solutions by explicit computation right? And now we say that on all R2 (because thats your region atm) there are no periodic solutions?! D has to be bounded, pretty sure that B(x, y) is unbouded if B:D-R ?!?

[johnkelly]

A two spices (dimension) Lotka-Volterra can display chaotic behaviour.

[RM.DATCHA]

i clicked on this guy thinking o this looks american