Cell cycle In Exercise 7.Review.25 a model for the cell cycle was introduced. It modeled
Chapter 10, Problem 26(choose chapter or problem)
Cell cycle In Exercise 7.Review.25 a model for the cell cycle was introduced. It modeled the concentrations of a molecule called MPF (maturation promoting factor) and another molecule called cyclin. MPF production is stimulated by cyclin, but the presence of MPF also inhibits its own production. Using M and C to denote the concentrations of these two biomolecules (in mgymL), the model for their interaction is dM dt C 1 CM 2 2 M 1 1 M dC dt 2 M (a) Suppose that 2, 1, 10, and 1. Find the only equilibrium. (b) Calculate the Jacobian matrix. (c) Determine the local stability properties of the equilibrium found in part (a) using the Jacobian from part (b). (d) Describe how M and C change near the equilibrium point.
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