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1987 A normal form for the Belousov-Zhabotinski reaction

Christophe LETELLIER
02/09/2018

The simple three-dimensional model

GIF - 1.4 ko

for describing the oscillations in the concentration of Ce ions was proposed by Françoise Argoul (University of Bordeaux) and co-workers. [1] A numerical integration of this model (Fig. 1b) produces a chaotic attractor whose template contains the three branches which were identified in the experimental data. [2] This model also captures the main characteristics of the experimental dynamics. When the parameter mu is varied, there is a period-doubling cascade leading to chaos. A unimodal chaotic attractor is shown in Fig. 1a : its shape has some similarities with the attractor observed by Harry Swinney and his colleagues [3] and topologically characterized by Gabriel Mindlin and Robert Gilmore [4]. The other parameter values are

GIF - 1 ko
JPG - 18.5 ko
Fig. 1. Three different behaviors produced by the 3D normal form for the BZ-reaction.

Experimental data corresponding to homoclinic chaos in the Belousov-Zhabotinski reacction and collected by Françoise Argoul are available here.

[1] F. Argoul, A. Arnéodo & P. Richetti, Experimental evidence for homoclinic chaos in the Belousov-Zhabotinsky reaction, Physics Letters A, 120 (6), 269-275, 1987.

[2] C. Letellier, J. Maquet, H. Labro, L. Le Sceller, G. Gouesbet, F. Argoul & A. Arnéodo, Analyzing chaotic behaviour in a Belousov-Zhabotinskii reaction by using a global vector field reconstruction, Journal of Physical Chemistry A, 102, 10265-10273, 1998.

[3] J. S. Turner, J. C. Roux, W. D. McCormick & H. L. Swinney, Alternating periodic and chaotic regimes in a chemical reaction - Experiment and theory, Physics Letters A, 85, 9-12, 1981.

[4] G. B. Mindlin & R. Gilmore, Topological analysis and synthesis of chaotic time series, Physica D, 58, 229-242, 1992.

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