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Interacting Oscillatory Chemical Reactors

Cohen, Donald S. and Neu, John C. (1979) Interacting Oscillatory Chemical Reactors. Annals of the New York Academy of Sciences, 316 . pp. 332-337. ISSN 0077-8923. doi:10.1111/j.1749-6632.1979.tb29478.x.

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We shall study the interaction of two oscillating systems of chemical reactions. In addition to the fundamental importance of these systems in chemical reactor theory, such systems often serve as models in biology, biochemistry, and ecology for the study of rhythms, synchronization, spatiotemporal control of various developmental processes, pattern formation, and population genetics. Experiments carried out by M. Marek and I. Stuchl and M. Marek and E. Svobodova on coupled chemical reactors clearly show that starting from a system of uncoupled nonlinear chemical oscillators there occur many different types of oscillatory solutions as the coupling and various other parameters change. In the next section we shall account for these observations via various perturbation and bifurcation techniques that clearly reveal the mechanisms and quantities that control the various phenomena and their bifurcations. The purpose of this paper is to present the results giving various physical and heuristic reasons but without detailed mathematical derivations. The full analysis can be found in the paper of J. C. Neu. Here we shall concentrate on the phenomena of synchronization and the bifurcation from this state to that known as rhythm splitting. Later we shall present and analyze a simple model for subharmonic response between coupled reactors with diffusion. In our simplest situation the coupling is assumed to occur as forcing on the boundary of one reactor as a result of oscillations in the other. We shall present the equations and the results only; the complete mathematical analysis and other results are presented in the paper of D. S. Cohen.

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Additional Information:© 1979 The New York Academy of Sciences. This work was supported in part by the U.S. Army Research Office under Contract DAHC-04-68-C-0006 and the National Science Foundation under Grant GP-32157X2.
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Army Research Office (ARO)DAHC-04-68-C-0006
Record Number:CaltechAUTHORS:20200113-133931375
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Official Citation:Cohen, D.S. and Neu, J.C. (1979), INTERACTING OSCILLATORY CHEMICAL REACTORS. Annals of the New York Academy of Sciences, 316: 332-337. doi:10.1111/j.1749-6632.1979.tb29478.x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100686
Deposited By: Tony Diaz
Deposited On:13 Jan 2020 21:51
Last Modified:16 Nov 2021 17:56

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