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Integrable Deformations and Dynamical Properties of Systems with Constant Population

Author

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  • Cristian Lăzureanu

    (Department of Mathematics, Politehnica University of Timişoara, Piața Victoriei 2, 300006 Timișoara, Romania)

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.

Suggested Citation

  • Cristian Lăzureanu, 2021. "Integrable Deformations and Dynamical Properties of Systems with Constant Population," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1378-:d:574643
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