University of California, Los Angeles

• LIFESCIENC 30B

• 0.0.0.1 Problem 4.3. Further Exercise 1 Exercise 4.3.FE 1 Briefly explain the statement due to W. Smith, “Puberty is a Hopf bifurcation.” What does this mean? It means that when the person is really young, certain hormones in the body remain at stable levels (i.e. one stable equilibrium point). When puberty hits, those levels are no longer stable at set values. Instead, the concentrations of hormones will display oscillating behavior as a function of time (i.e. the appearance of a limit cycle attractor). Revised Summer 2020 LS 30 Solutions Manual Click Here to Go To TOC 1 0.0.0.1 Problem 4.3. Further Exercise 6 Exercise 4.3.FE 6 Recall the Higgins-Selkov model of glycolysis, S 0 = V0 − cSP2 P 0 = cSP2 − kP a) Simulate this model with V0 = 0.5, c = 0.23, and k = 0.4 for three different initial conditions. How does the system behave? b) In real life, for these parameter values, V0 can range from 0.48 to 0.6. Using any method you choose, approximate the value of V0 at which the system begins to have persistent oscillations. (You may want to use more than one method.) Part a: Simulate this model with V0 = 0.5, c = 0.23, and k = 0.4 for three different initial conditions. How does the system behave? (Please note that there is more than one possible set of solutions to this problem) We will use the following three initial conditions: (S = 4, P = 1), (S = 3, P = 4), and (S = 1, P = 2). Our codes will look something like this: 1 var (‘S, P’) 2 V0 = 0.5 3 c = 0.23 4 k = 0.4 5 6 Sprime(S, P) = V0 - c * S * Pˆ2 7 Pprime(S, P) = c * S * Pˆ2 - k * P 8 t list = srange( 0, 20