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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Philosophical Transa...arrow_drop_down
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Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences
Article . 1992 . Peer-reviewed
License: Royal Society Data Sharing and Accessibility
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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Multistability, oscillations and travelling waves in a product-feedback autocatalator model. I. The well-stirred system

Multistability, oscillations and travelling waves in a product-feedback autocatalator model. I: The well-stirred system
Authors: Collier, S. M.; Merkin, J. H.; Scott, S. K.;

Multistability, oscillations and travelling waves in a product-feedback autocatalator model. I. The well-stirred system

Abstract

Abstract The behaviour of a modified autocatalator model: P + C → A + C, rate = k0pc, A + 2B → 3B, rate = k1ab2, B → C, rate = k2b, C → D , rate = k3c, is studied in a batch system with the 'pool chemical approximation’ applied to the precursor P (i.e. we assume p = p0 = constant for all time). Only for the special case k0p0 = k3, for which there is a reduction to a two variable system, are ‘classical’ nonlinear dynamical responses exhibited, with multiple stationary states, Hopf bifurcation to stable or unstable limit cycles and extinction of oscillations via homoclinic orbit formation. Under limiting parameter values, the locus of homoclinic bifurcations can be obtained analytically. For the general cases of k0p0 < k3 and k3p0 > k3 the system is contracting or expanding respectively. For the contracting case, there may be an initial period of sustained but strictly transient bistability or oscillation, and a clear three-time period emerges, before the reaction dies out completely, with b and c tending to zero. For the expanding case, the reaction either dies out as above or follows a continuous growth in intermediate species concentrations and overall reaction rate. The behaviour in these general cases can be readily understood in great detail from a consideration of the stationary state and dynamic bifurcation structure for the reduced case.

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Keywords

chemical wave propagation, multistability, double zero eigenvalue degeneracy, Hopf bifurcation, product-feedback autocatalator scheme, homoclinic orbit bifurcations, Classical flows, reactions, etc. in chemistry, extinction of oscillations, stationary state, limit cycle structure

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
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