An Interdisciplinary Journal

* 2000, Volume 3, Number 3, pp.242--246*

Some object problems concerning the redistribution of common resource,
upon being formalized, lead to skew-symmetric three-dimensional (3D)
Lotka-Volterra systems (LVS) with an additive planar first integral
relevant to the conservation of that re-source. If the domain of
variables is extended to the negative range, one can construct an
atlas of solutions based on the classes of equivalence connected with
solution diffeomorphism. That division entails the division of the system
coefficient space into zones. Each point belonging to a zone defines the
system and the family of its solutions in the solution space. The physical
meaning of the ratios of the system coefficients can be understood as a
measure of "coherence" of the swapping between its constituents. The
maximum of coherence corresponds to equality to unity of absolute values
of those ratios. For 3D LVS with an antisymmetric right-hand side, the
projective properties of functional space and the space of its parameters
with respect to families of the integral curves in functional space are
investigated.

*Key words: *nonlinearity, conservation law, skew-symmetry,
projective properties, oscillations, election.

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Last updated: *June 16, 2001*