The Györgyi-Field Model for the Belousov-Zhabotinsky Reaction

The Belousov–Zhabotinsky (BZ) reaction in a continuous-flow stirred-tank reactor (CSTR) can exhibit chaos, contrary to the Oregonator model, which has no chaotic solutions.

Deterministic chaos in the BZ reactor was studied in [1]. The scaled differential equations are:

,

,

,

,

where , , , and and the significance of all parameters ( for , , , , , , , , , and ) is given in [1].

Here, the bifurcation parameter is , the inverse of the reactor's residence time.

Snapshots 6 and 7: finally back to period-2 and periodic behavior for and , respectively.

This bifurcation diagram (a remerging Feigenbaum tree) given below was obtained by the authors using a separate program that draws on the present Demonstration. A close look at this bifurcation diagram confirms the findings seen in the various snapshots given above.

References

[1] L. Györgyi and R. J. Field, "A Three-Variable Model of Deterministic Chaos in the Belousov-Zhabotinsky Reaction," Nature, 355, 1992 pp. 808–810. doi:10.1038/355808a0.