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Karavaev A. D., Ryzhkov A. B., Kazakov V. P. Birth and death of fractal tore in the Belousov - Zhabotinsky reaction model. Izvestiya VUZ. Applied Nonlinear Dynamics, 2001, vol. 9, iss. 1, pp. 89-100. DOI: 10.18500/0869-6632-2001-9-1-89-100
Birth and death of fractal tore in the Belousov - Zhabotinsky reaction model
The mechanism of birth and destruction of chaotic toroidal attractor — fractal tore — is investigated for the 11—stage Belousov — Zhabotinsky reaction model. It is revealed, that fractal tore emerges as а result of period—doubling bifurcations cascade of а resonant state оп torus, and disappears through type I intermittency. Constructed bifurcation diagram shows, that fractal toris exist in a wide enough range, where resonant states, fractal toris and areas of intermittency appear conformingly in turn. It gives the basis to believe, that observed model dynamics, as the Belousov — Zhabotinsky reaction itself, involves two fundamental frequencies, and that the evolution of described regimes occurs on torus upon general tendency of rotation number to reduction.
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