Belousov-Zhabotinsky reaction chaos

Basin of attraction, see Attraction basin Bell-shaped dependence, of Ca release on Ca, 358,359,379,499 Belousov-Zhabotinsky reaction chaos, 12,283,511 chemical waves, 169,513 excitability, 102,213 oscillations, 1,508 temporal and spatiotemporal organization, 7,169 Bifurcation... 

Gyorgyi L and Field R J 1992 A three-variable model of deterministic chaos in the Belousov-Zhabotinsky reaction Nature 355 808-10... 

L. Gybrgyi and R.J. Field, Simple-Models of Deterministic Chaos in the Belousov-Zhabotinsky Reaction, J. Phys. Chem. 95 (1991) 6594-6602. 

Petrov, V., V. Gaspar, J. Masere K. Showalter. 1993. Controlling chaos in the Belousov-Zhabotinsky reaction. Nature 361 240-3. 

Roux, J.C. 1983. Experimental studies of bifurcations leading to chaos in the Belousov-Zhabotinsky reaction. Physica 7D 57-68. 

Tomita, K. I. Tsuda. 1979. Chaos in the Belousov-Zhabotinsky reaction in a flow system. Phys. Lett. 71A 489-92. 

Zhang, D., L. Gyorgyi W.R. Peltier. 1993. Deterministic chaos in the Belousov-Zhabotinsky reaction Experiments and simulations. Chaos 3 723 5. 

Gydrgyi, L, Field, R, J. 1992. A Three-Variable Model of Deterministic Chaos in the Belousov-Zhabotinsky Reaction, Nature 355, 808-810,... 

Petrov, V. Caspar, V. Masere, J, Showalter, K, 1993, Controlling Chaos in the Belousov-Zhabotinsky Reaction, Nature 361, 240-243,... 

Michelson, D. M., Sivashinsky, G. I. (1977) Nonlinear analysis of hydrodynamic instability in laminar flames - II. Numerical experiments. Acta Astronautica 4, 1207 Moon, H. T., Huerre, P., Redekopp, L. G. (1982) Three-frequency motion and chaos in the Ginzburg-Landau equation. Phys. Rev. Lett. 49, 458 Murray, J. D. (1976) On travelling wave solutions in a model for the Belousov-Zhabotinsky reaction. J. Theor. Biol. 56, 329... 

The Belousov-Zhabotinsky reaction shows oscillations of great variety and complexity it even exhibits chaos. In chaotic systems arbitrarily close initial conditions diverge exponentially the system exhibits aperiodic behavior. A... 

Various scenarios to "strange attractor" like behavior have been experimentally observed in the Belousov-Zhabotinsky reaction in an open flow system, i.e. a continuous stirred tank reactor Cll-193. We propose a global interpretation of these transitions to chaos in terms of the competition between three instabilities. In the neighborhood of the polycritical surface we study the normal form which describes this interaction. We limit our investigation to experimental paths which are characteristic of the variety of dyncimical behavior one can encounter in this region of paraoneter space. 

Nonlinear Interactions Between Instabilities Leading to Chaos in the Belousov-Zhabotinsky Reaction. By F. Argoul, P. Richetti, and A. Arneodo. .. 146... 

Belousov-Zhabotinsky reaction when conducted in a well-mixed medium [91, 92, 95]. The so-called chemical chaos and its homoclinic nature was shown to arise from the nonlinear complexity of the chemical kinetics. The remarkable feature of the homoclinic intermittent bursting illustrated in Figures 9 to 12, is that it results from the interaction of the diffusion process with a chemical reaction which itself would proceed in a stationary manner if diffusion was negligible. 

The peroxidase reaction provides another prototype for periodic behaviour and chaos in an enzyme reaction. As noted by Steinmetz et al. (1993), in view of its mechanism based on free radical intermediates, this reaction represents an important bridge between chemical oscillations of the Belousov-Zhabotinsky type, and biological oscillators. In view of the above discussion, it is noteworthy that the model proposed by Olsen (1983), and further analysed by Steinmetz et al. (1993), also contains two parallel routes for the autocatalytic production of a key intermediate species in the reaction mechanism. As shown by experiments and accounted for by theoretical studies, the peroxidase reaction possesses a particularly rich repertoire of dynamic behaviour (Barter et al, 1993) ranging from bistability (Degn, 1968 Degn et al, 1979) to periodic oscillations (Yamazaki et al, 1965 Nakamura et al, 1969 ... 

C. VIDAL, Le chaos dans la reaction de Belousov-Zhabotinsky, dans "Le chaos theories et experiences" (P. Berge, 6d.). Hasson, Paris, 1987. 

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