The role of four regulatory hormones in controlling testicular function in a delay model

Our proposed mathematical model for the secretion in hypothalamus-pituitary-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 which accounts for the pulsatile release of these hormones. We have derived the conditions for local asymptotic stability of the steady state and have estimated the length of delay to preserve the stability. Regions for stability and oscillations of the system are given in K − τ and m − τ plane, and the role of Inhibin in regulating the male fertility status by altering the FSH level has been clearly shown by computer simulation of the model.