3. A simplified differential equation model for glycolysis is known as the glycolytic oscillator: dx 8- kr - xy? dt dy kx + xy- - y dt where a represents fructose (fructose-6-phosphate) and y represents ADP (adeno- sine triphosphate). Note that r and y are scaled concentrations and the parameters 8 and k are positive numbers. Write an R script that numerically integrates the gly- colytic oscillator model and graphs the solution for both variables. Assume that the parameter k = 0.1 and the initial conditions are any random number between 0 and 1. (a) Simulate the model for d = 0.2 and 8 = 0.6 until t = 50. Describe and compare the dynamics of the two cases. (b) By varying the parameter 8 in your simulations, try to find any bifurcation points (values of d) at which the qualitative long-term behavior changes