Kinetic equations of reactions without diffusion

In the following sections a number of mechanisms corresponding both to real and to hypothetical reactions will be described and the respective kinetic equations given. The sequence of models to be discussed corresponds essentially to their increasing complexity. A part of the models under discussion have been examined in a similar sequence by Ebeling. 

In principle it can be stated that kinetic equations containing one state variable may represent stationary states, autocatalytic processes and the phenomena related to multistability. Equations in two variables can describe periodical oscillations with time and periodical spatial structures (accounting for diffusion). Equations in three variables enable a description of chaotic processes. State variables are the reagent concentrations and, when diffusion is taken into account, additional state variables associated with the wavelengths of waves propagating in solution appear. 

The models selected below permit us to represent all the phenomena mentioned above or, more specifically, to describe the transition of a system from a stable stationary state, by way of its destabilization, to a new stable state of a different type of dynamics. 

The examined systems have three types of sensitive states  

After determining a sensitive state we will be able to predict, on the basis of the corresponding standard form, the most general dynamics possible in the investigated system and that related to catastrophes. 

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