Chaos in a bienzymatic cyclic model with two autocatalytic loops

A general bienzymatic cyclic system including two autocatalytic loops is studied and used as a basic design principle for modelling extracellular matrix turnover. Using classical enzyme kinetic rates, the model is described by a set of four ordinary differential equations and numerically studied by bifurcation diagrams and Poincaré sections. We observe limit-cycle oscillations and chaotic behaviors arising from period-doubling cascades or intermittency. Chaotic oscillations originate from distinct strange attractors that undergo boundary and internal crisis. For some parameter values, the system presents several bistable areas, where a limit cycle coexists with another one or with a strange attractor. The dynamics are qualitatively modified when the weight of the autocatalytic loops on the system varies, resulting in the change in the number of attractors.