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In class, we analyzed a model of glycolysis: i = -x + ay + ²y, ý = b – ay – x²y . Show that solutions of this ODE are confined to the set Q = {(r, y) E R² | a20,0 0 around (b, b/(a + b²)), with ɛ being very small. Are we guaranteed that Q = Q\ B would contain a closed trajectory?

In class, we analyzed a model of glycolysis: i = -x + ay + ²y, ý = b – ay – x²y . Show that solutions of this ODE are confined to the set Q = {(r, y) E R² | a20,0 0 around (b, b/(a + b²)), with ɛ being very small. Are we guaranteed that Q = Q\ B would contain a closed trajectory?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In class, we analyzed a model of glycolysis: i = -x + ay + ²y, ý = b – ay – x²y . Show that solutions of this ODE are confined to the set Q = {(r, y) E R² | a20,0<y < b/a}. Does this result imply the existence of a closed trajectory inside Q? Now let B the ball of radius ɛ > 0 around (b, b/(a + b²)), with ɛ being very small. Are we guaranteed that Q = Q\ B would contain a closed trajectory?
Transcribed Image Text:In class, we analyzed a model of glycolysis: i = -x + ay + ²y, ý = b – ay – x²y . Show that solutions of this ODE are confined to the set Q = {(r, y) E R² | a20,0<y < b/a}. Does this result imply the existence of a closed trajectory inside Q? Now let B the ball of radius ɛ > 0 around (b, b/(a + b²)), with ɛ being very small. Are we guaranteed that Q = Q\ B would contain a closed trajectory?
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