THE ROLE OF 4 REGULATORY HORMONES IN CONTROLLING TESTICULAR FUNCTION IN A DELAY MODEL

Our proposed mathematical model for the secretion in hypothalamus-pitu itary-gonadal axis introduces four regulatory hormones viz. GnRH, FSH, Testosterone, and Inhibin. Here, we have considered four dimensional delay differential equations with multiple negative feedback loops whi ch accounts for the pulsatile release of these hormones. We have deriv ed the conditions for local asymptotic stability of the steady state a nd have estimated the length of delay to preserve the stability. Regio ns for stability and oscillations of the system are given in K - tau a nd m - tau plane, and the role of Inhibin in regulating the male ferti lity status by altering the FSH level has been clearly shown by comput er simulation of the model.