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Zusammenfassung:
A two-variable/two-compartment model of enzyme-induction with regulated diffusion produces spatial chaos. In a bichaotic state two symmetrical attractors coexist, each with a constant polarity between the cells. Collision and overlap between the attractors forms a singular attractor which is characterized by an irregularly switching polarity, thereby producing apparently random sequences of time periods. The mean period length obeys a scaling law with the bifurcation parameter. Examination of next-amplitude maps using symbolic representation of the system evolution reveals the existence of a fractal “boundary” inside the attractor. A cubic map analogue of the differentiable system is studied in parallel. A scaling function for the uncertainty exponent of the fractal boundary in the cubic map is proposed.
