Abstract
By definition, any self-replicating chemical system is autocatalytic, so that its kinetics will be non-linear. Non-linearity is a necessary condition for the existence of chemical oscillations and for complex behaviour in general. In this paper, we discuss the basic principles underlying such phenomena and their theoretical analysis. We believe that wider familiarity with these techniques will assist the interpretation of experimental observations on non-linear chemical reactions, including self-reproducing systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Amit, D. 1989. Modelling brain function. The world of attractor neural networks. Cambridge: Cambridge University Press.
Babloyantz, A. 1986. Molecules, dynamics and life. New York: Wiley.
Bachmann, P. Luisi, P L. Lang J. 1992. Autocatalytic self-replicating micelles as models for prebiotic structures. Nature 357: 57–59.
Billingham J, Coveney P. 1993. Simple chemical clock reactions: Application to cement hydration. Journal of the Chemical Society, Faraday Transactions 89(16): 3021–3028.
Billingham J, Needham, D. 1992. Mathematical modelling of chemical clock reactions.I. Induction, inhibition and the iodate-arsenous-acid reaction Philosophical Transactions of the Royal Society of London Series A 340: 569–591.
Billingham J, Needham, D. 1993. Mathematical modelling of chemical clock reactions.2. A class of autocatalytic clock reaction schemes. Journal of Engineering Mathematics 27:113–145.
Chaudry A, Coveney P, Billingham J. 1994. Exploring complexity in some simple non linear chemical kinetic schemes. Journal of Chemical Physics (in press).
Chay T R. 1985. Chaos in a 3-variable model of an excitable cell. Physica D 16: 233–242.
Chay T R, Rinzel J R. 1985. Bursting, beating, and chaos in an excitable membrane model. Journal of Biophysics 47: 357–366.
Coveney P. 1988. The second law of thermodynamics: Entropy, irreversibility and dynamics. Nature 333: 409–415.
Coveney P, Chaudry A. 1992. Quantifying chaos and transient chaos in nonlinear chemically reacting systems. Journal of Chemical Physics 97: 7448–7458.
Coveney P, Highfield R. 1992. The Arrow of Time. London: Harper Collins.
Coveney P, Evans A. 1994. Canonical non-equilibrium ensembles and subdynamics. Journal of Statistical Physics (in press).
Feigenbaum M. 1978. Journal Statistical Physics 19: 25–52.
Diem CB, Hudson JL. 1987. Chaos during the elctrodissolution of iron. AICHE Journal 3: 218–224.
Doedel E. 1986. AUTO-Continuation and Bifurcation Problems in Ordinary Differential Equations. Pasadena: California Institute of Technology.
Glansdorff P, Prigogine I. 1971. Thermodynamic Theory of Structure, Stability and Fluctuations. New York: Wiley.
Gray P, Scott, S. 1990. Chemical Oscillations and Instabilities. Oxford: Clarendon Press.
Guckenheimer J, Holmes P. 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Berlin: Springer.
Koper MT, Gaspard P. 1992. The modelling of mixed-mode and chaotic oscillations in elctrochemical systems. Journal of Chemical Physics 96, 7797–7813.
Lev O, Wolfberg A, Sheintuch M, and Pismen LM. 1988. Bifurcations to periodic and chaotic motions in anodic nickel dissolution. Chemical Engineering Science 43: 1339–1353.
Maselko J, Swinney H L. 1986. Complex periodic oscillations and Farey arithmetic in the Belousov-Zhabotinskii reaction. Journal of Chemical Physics 85, 6430–6441.
Mathematica Version 2.1. 1992. Champaign, Illinois: Wolfram Research Inc.
Nicolis G, Prigogine I. 1977. Self-Organisation in Non-Equilibrium Systems. New York: Wiley.
Nicolis G, Prigogine I. 1989. Exploring Complexity. New York: W H Freeman.
Pomeau Y, Manneville P. 1980. Intermittent transition to turbulence in dissipative dynamical systems. Communications in Mathematical Physics 74: 189.
Ruelle D. 1973. Some comments on chemical oscillations. Transactions of the New York Academy of Sciences 35: 66–71
Ruelle D. 1990. Deterministic chaos-the science and the fiction. Proceedings of the Royal Society of London A427: 241–248.
Ruelle D, Takens F. 1971. On the nature of turbulence. Communications in Mathematical Physics 20: 167–192.
Scott S. 1991. Chemical Chaos. Oxford: Oxford University Press.
Tyson J. 1976. The Belousov-Zhabotinski reaction. Heidelberg: Springer-Verlag.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Coveney, P. (1994). Chemical Oscillations and Non-Linear Chemical Kinetics. In: Fleischaker, G.R., Colonna, S., Luisi, P.L. (eds) Self-Production of Supramolecular Structures. NATO ASI Series, vol 446. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0754-9_14
Download citation
DOI: https://doi.org/10.1007/978-94-011-0754-9_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4324-3
Online ISBN: 978-94-011-0754-9
eBook Packages: Springer Book Archive