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...

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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? $

Extracted 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< 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?

Jun 03, 2022

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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...

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