Integrable and non-integrable Lotka-Volterra systems
Bountis T. Zhunussova Z. Dosmagulova K. Kanellopoulos G.
28 June 2021Elsevier B.V.
Physics Letters, Section A: General, Atomic and Solid State Physics
2021#402
In a recent paper [1], completely integrable cases were discovered of the Lotka Volterra Hamiltonian (LVH) system without linear terms, [Formula presented], aij=−aji, satisfying the condition H=∑i=1nxi=h=const. In this paper, we first generalize this system to one that includes an arbitrary set of linear terms that preserve the Hamiltonian integral. We thus discover a wide class of LVH systems which we claim to be integrable, since their equations possess the Painlevé property, i.e. their solutions have only poles as movable singularities in the complex t-plane. Next, we focus on the case n=3 and vary some of the parameters, including additional nonlinearities to look for nonintegrable extensions with interesting dynamical properties. Our results suggest that, in this class of systems, non - integrability generally yields simple dynamics far removed from the type of complexity one expects from non - integrable 3 - dimensional nonlinear systems.
Integrable systems , Lotka-Volterra , Nonintegrability , Painlevé property
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Centre of Integrable Systems, P.G. Demidov Yaroslavl State University, Russian Federation
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Department of Mathematics, University of Patras, Patras, 26500, Greece
Centre of Integrable Systems
Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University
Department of Mathematics
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