Verifications and falsifications of traditional beliefs

The trajectory of a general autonomous system of differential equations can wander anywhere in the state-space. What kind of restrictions are obtained if one considers the trajectories of a kinetic differential equation It was mentioned earlier (Subsection 4.1.2) that the solutions of a kinetic differential equation remain in the first orthant if they started there. More refined statements regarding positivity and nonnegativity have also been stated as Problem 6 of Subsection 4.1.4. Now let us try to delineate an as narrow as possible set in the state-space for the trajectories. As a next step towards this goal let us write the kinetic differential equation (4.6) in the form 

This formula expresses the fact that x(t) - Xq lies in the linear space of the column vectors of 

Let us consider an example. The kinetic differential equation of the reaction 

The meaning of the result above can be seen in Fig. 4.1, which shows the set, , of positive equilibrium points that is now a parabola. This parabola intersects at a unique point the part of 

It would be desirable if a general sufficient condition ensuring quasi-ihermodynamic behaviour was formulated and related to the mechanism. 

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