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Necessary conditions for the existence of quasi-polynomial invariants: the quasi-polynomial and Lotka-Volterra systems. (English) Zbl 0928.37002

Summary: The authors show that any quasi-polynomial invariant of a quasi-polynomial dynamical system can be transformed into a quasi-polynomial invariant of a homogeneous quadratic Lotka-Volterra dynamical system. They show how this quasi-polynomial invariant can be decomposed in a simple manner. This decomposition permits to conclude that the existence of polynomial semi-invariants in Lotka-Volterra systems is a necessary condition for the existence of quasi-polynomial invariants. The authors derive a method which allows to construct necessary conditions for the existence of semi-invariants on Lotka-Volterra dynamical systems. Applications are given.

MSC:

37C99 Smooth dynamical systems: general theory
34A34 Nonlinear ordinary differential equations and systems

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References:

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