YoVDO

Limit Cycles - Poincare-Bendixson Worked Examples: Glycolysis

Offered By: Ross Dynamics Lab via YouTube

Tags

Aerospace Engineering Courses Differential Equations Courses Dynamical Systems Courses Nonlinear Dynamics Courses Oscillations Courses Glycolysis Courses

Course Description

Overview

Explore the application of the Poincaré-Bendixson theorem in proving the existence of limit cycles through worked examples, including a biochemical oscillator model of glycolysis. Delve into the construction of trapping regions guided by nullclines, and examine the implications of the theorem for two-dimensional differential equation systems. Gain insights into analytical examples in polar coordinates, nullcline analysis, and the identification of parameter regions where stable limit cycles exist. Understand the significance of this theorem in ruling out chaotic behavior in 2D systems and its relevance to biological oscillations.

Syllabus

Review of Poincare-Bendixson theorem.
Analytical example in polar coordinates.
Biological example: glycolysis.
Nullclines.
Trapping region for biochemical oscillator model.
Region in parameter space where stable limit cycle exists.


Taught by

Ross Dynamics Lab

Related Courses

Understanding Biological Energy
Royal Holloway, University of London via FutureLearn
Biochemistry
Shomu's Biology via YouTube
Metabolism - Glycolysis
Ninja Nerd via YouTube
Cellular Respiration
The Organic Chemistry Tutor via YouTube
Inborn Errors of Metabolism - Dr. Tumelo Satekge
The Royal College of Pathologists via YouTube