Journal of Mathematical Chemistry

, Volume 27, Issue 1–2, pp 71–88 | Cite as

Chemical systems consisting only of elementary steps – a paradigma for nonlinear behavior

  • Thomas Wilhelm


We present a new analytic method which allows one to interpret a mass‐action kinetic reaction of arbitrary molecularity as the limit case of a sequence of bimolecular steps. Together with other technics (transformation of an arbitrary ODE into a polynomial ODE [8]; transformation of a polynomial ODE into a form which can be interpreted as a mass‐action kinetic system [10]), it is thus possible to construct an at most bimolecular mass‐action kinetic system with the same dynamic behavior as an arbitrary ODE. Furthermore, we demonstrate necessary improvements of the transformation given in [10]. Is is also shown that an arbitrary single mass‐action kinetic reaction can be understood as a sequence of two reactions with a short‐living intermediate. In particular, it therefore follows that an autocatalytic reaction can always be approximated by two nonautocatalytic ones without changing the dynamics of the whole system.


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© Kluwer Academic Publishers 2000

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  • Thomas Wilhelm

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