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arXiv · 1106.0805

Integrable deformations of Lotka-Volterra systems

Angel Ballesteros·Alfonso Blasco·Fabio Musso
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Abstract

The Hamiltonian structure of a class of three-dimensional (3D) Lotka-Volterra (LV) equations is revisited from a novel point of view by showing that the quadratic Poisson structure underlying its integrability structure is just a real three-dimensional Poisson-Lie group. As a consequence, the Poisson coalgebra map that is given by the group multiplication provides the keystone for the explicit construction of a new family of 3N-dimensional integrable systems that, under certain constraints, contain N sets of deformed versions of the 3D LV equations. Moreover, by considering the most generic Poisson-Lie structure on this group, a new two-parametric integrable perturbation of the 3D LV system through polynomial and rational perturbation terms is explicitly found.

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Angel Ballesteros, Alfonso Blasco, Fabio Musso. 2011-08-22. Integrable deformations of Lotka-Volterra systems. https://doi.org/10.1016/j.physleta.2011.07.055

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