An Interdisciplinary Journal

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

Around Lotka-Volterra Kind Equations and Nearby Problems.
V.M. Dubovik, A. G. Galperin, V. S. Richvitsky

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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