The Györgyi-Field Model for the Belousov-Zhabotinsky Reaction

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.


Contributed by: Housam Binous, Brian G. Higgins, and Ahmed Bellagi (January 2013)
Open content licensed under CC BY-NC-SA



The snapshots show several situations.

Snapshot 1: periodic behavior for

Snapshot 2: period-2 for

Snapshot 3: period-3 for

Snapshot 4: period-5 for

Snapshot 5: chaos for

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.


[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.

[2] A. Barnett, "Math 53: Chaos! - Fall 2011." (Jan 14, 2013)

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.