Integrable Deformations and Dynamical Properties of Systems with Constant Population

Cristian Lăzureanu
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Cristian Lăzureanu: Department of Mathematics, Politehnica University of Timişoara, Piața Victoriei 2, 300006 Timișoara, Romania

Mathematics, 2021, vol. 9, issue 12, 1-13

Abstract: In this paper we consider systems of three autonomous first-order differential equations x ? = f ( x ) , x = ( x , y , z ) , f = ( f 1 , f 2 , f 3 ) such that x ( t ) + y ( t ) + z ( t ) is constant for all t . We present some Hamilton–Poisson formulations and integrable deformations. We also analyze the case of Kolmogorov systems. We study from some standard and nonstandard Poisson geometry points of view the three-dimensional Lotka–Volterra system with constant population.

Keywords: Hamilton–Poisson systems; integrable deformations; Lotka–Volterra systems; Kolmogorov systems; stability; periodic orbits; heteroclinic orbits (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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