Bifurcation and chaos of a discrete-time mathematical model for tissue inflammation (Q258123)

The authors consider a model for tissue inflammation dynamics comprising two first-order, nonlinear, ordinary differential equations, containing four parameters. They then discretise time using the forward Euler method to obtain a discrete time map. Using standard centre manifold calculations, the fixed points of this map are found and conditions for saddle-node, period-doubling and Hopf bifurcations of fixed points are found. They also show that the model has chaotic behaviour in the sense of Marotto (a fixed point is a snap-back repeller). The paper concludes with numerical confirmation of their results, using large time-step sizes.