Limit Cycles, Part 3: Poincare-Bendixson Worked Examples- Glycolysis

Poincaré-Bendixson theorem is used to prove the existence of a limit cycle in two examples, including a biochemical oscillator, glycolysis, for certain values of the parameter. We carefully construct the necessary trapping region, guided by nullclines. We comment on the implication of the Poincare-Bendixson theorem for the absence of chaos in 2-dimensional differential equation systems.

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► Chapters

0:00 Review of Poincare-Bendixson theorem
1:27 Analytical example in polar coordinates
7:33 Biological example: glycolysis
9:44 Nullclines
14:50 Trapping region for biochemical oscillator model
24:00 Region in parameter space where stable limit cycle exists


References:
Steven Strogatz, "Nonlinear Dynamics and Chaos", Chapter 7: Limit Cycles




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