## Kinetical systems.(English)Zbl 0903.34043

The system $\frac {dy}{dx} = AG(t,y), \quad (t,y) \in \mathbb{R} \times \mathbb{R}^n \tag $$*$$$ occuring in physical chemistry and biology is investigated. Here is $$A:=C-C'$$ where $$C,C'$$ are $$n\times m$$ matrices whose elements $$c_{ij}$$, $$c'_{ij}$$ are nonnegative integers such that rank$$(A)<m$$ and $$G: = [G_j]$$ is an $$m$$-vector $G_j (t,y) : = -r_j(t) \prod ^n_{k=1} y_k^{c_{kj}} + d_j (t) \prod ^n_{k=1} y_k^{c_{kj}'}.$ It is supposed that $$r_j$$, $$d_j : \mathbb{R} \rightarrow [0,\infty)$$ are continuous functions.
Using the method of inequalities, the elementary fixed point method and the invariance principle the author derives some basic properties of nonnegative solutions to the nonautonomous system $$(*)$$, proves the existence of a critical point in the autonomous case and derives some asymptotic properties of a special form of $$(*)$$.
Reviewer: M.Ráb (Brno)

### MSC:

 34D05 Asymptotic properties of solutions to ordinary differential equations 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.) 92E20 Classical flows, reactions, etc. in chemistry
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### References:

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