... tex2html_wrap_inline2028  
In order to simplify the notation we do not write explicitely the dependence of the concentrations on tex2html_wrap_inline2124 , but actually the concentrations are functions of both tex2html_wrap_inline2124 , T and tex2html_wrap_inline2024 .
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...constant 
E.J. Hinch, Perturbation Methods (Cambridge University Press, Mexico, 1992), p. 116.
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...stable 
Given that (20) defines a continuum of fixed points, they are all ``marginally'' stable, in the sense that the linearization of the dynamical system around any of them has a zero eigenvalue. However, the system also has N constants of motion so that only one fixed point belongs to each level set of these N constants. We discuss this in detail in Sec. III.
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... tex2html_wrap_inline1954  
Notice that the right-hand-sides of Eqs. (25)-(26) correspond to a linearization of the system (10)-(11) around a fixed point given by (20). As mentioned before, this linearized operator has eigenvalues equal to zero. Requiring that tex2html_wrap_inline2594 for all i is equivalent to saying that the solutions , tex2html_wrap_inline2294 do not have any component along the directions associated with these zero eigenvalues.

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...in
J.E. Pearson, and W. Bruno, Chaos 2, 513 (1992); S. P. Dawson, A. Lawniczak, and R. Kapral, J. Chem. Phys. 100, 5211 (1994)
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...model 
E. E. Selkov, European J. Biochem. 4, (1968),p. 79-86.
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...in 
L. A. Segel and M. Slemrod, SIAM Rev. 3, (1989), p.466-477.
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...in 
E.C. Edblom, M. Orban, and I.R. Epstein, J. Am. Chem. Soc. 108, 2826 (1986)
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...in 
K.J. Lee, W.D. McCormick, Q. Ouyang, and H.L. Swinney, Science 261, 192 (1993); K.J. Lee, W.D. McCormick, J.E. Pearson, and H.L. Swinney, Nature 369, 215 (1994); K.J. Lee, and H.L. Swinney, Phys. Rev. E 51, 1899 (1995)
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...in 
V. Gáspár, and K. Showalter, J. Phys. Chem. 94, 4973 (1990)
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.

Silvina Ponce Dawson
Fri Aug 27 03:50:25 ART 1999