Qualitative study of ordinary differential equations

Chemical processes in condensed media often cannot be reduced to simple mono- and bimolecular reactions simply because chains of reaction take place. Therefore their kinetics is described by a set of ordinary differential equations (2.1.1) which are generally nonlinear due to bimolecular stages. Independent variables nft), i = l.s (intermediate reactions products) define a number of equations under study. 

Solutions nft) of the set (2.1.1) depend on the initial conditions only because reaction rates are constant. 

For a qualitative description of kinetics, of great interest are both asymptotical t -y oo) solutions independent on initial conditions and how particular solutions approach them. Complicated systems can reveal several such asymptotic solutions. Initial conditions define a choice of one of several possible asymptotic solutions. A general scheme for investigating a set of ordinary differential equations was very well described in a number of monographs [4, 7, 14-16] it includes  

Obviously, if as f - oo the stationary solution drift)/dt = 0 exists, indeed the asymptotic solution nfoo) of (2.1.1) is one of the solutions n of the set (2.1.14). Here we have an example of a simple but very important case of a stable stationary solution. Other stationary points cannot be ascribed to the asymptotic solutions, i.e., n° f nfoo), but they are also important for the qualitative treatment of the set of equations. Note that striving of the solutions for stationary values is not the only way of chemical system behaviour as t - oo another example is concentration oscillations [4, 7, 16]. Their appearance in a set (2.1.2) depends essentially on a nature of 

Stationary points, mentioned above. An asymptotic solution of the oscillating type is connected with the concept of the limit cycle. Complicated chemical systems reveal also irregular or chaotic concentration oscillations [8], 

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