Chaos, coexistence of attractors and fractal basin boundaries of attraction in a model system coupling activation and inhibition in parallel

The dynamical behaviour of a theoretical model featuring activation and inhibition coupled in parallel is studied in two different parameter regions. The coexist- ence of attractors between various complex oscillations and between period-2 oscillation and chaos has been found. Coexisting period-1 and other periodic attractors are also observed. A range of bifurcation behaviours is found, including periud duubling cascades to chaos and the existence of two period-1 regimes produced from sub- and super-critical Hopf bifurcations respectively. For the coexisting attractors, the fractal basin boundaries of attraction are observed. Finally, we discuss the implications of the model for enzymatic reactions