Bifurcations and chaos in a model biochemical reaction pathway

Control mechanisms in the form of positive and negative feedback loops are responsible for the sensitivity and stability in the coherent behavior of the spatio-temporal organization in living cells. Models of these networks involving such feedback mechanisms have been shown to exhibit a rich spectrum of dynamical behaviors. A network involving both positive and negative feedbacks was earlier investigated by Sinha and Ramaswamy [1987]. We obtain a phase diagram of the possible dynamical behaviors for this model. Further, we investigate the origin and properties of the complex oscillations in the model. A simpler system is derived and shown to possess similar dynamical behaviors. Avenues for further investigation of the system with respect to relevant variations in some of the parameter values are suggested.