Periodic solutions and chaos in a non-linear model for the delayed cellular immune response

We model the cellular immune response using a set of non-linear delayed differential equations. We observe that the stationary solution becomes unstable above a critical immune response time. The exponents characterizing the approach to this bifurcation point as well as the critical slow dynamics are obtained. In the periodic regime, the minimum virus load is substantially reduced with respect to the stationary solution. Further increasing the delay time, the dynamics display a series of bifurcations evolving to a chaotic regime characterized by a set of 2D portraits.