Integrable Deformations and Dynamical Properties of Systems with Constant Population

In this paper we consider systems of three autonomous first-order differential equations x=f(x), x=(x,y,z),f=(f1,f2,f3) 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.

Automated summary

The paper investigates systems of three autonomous first-order differential equations under the condition that x(t)+y(t)+z(t) is constant for all t. It presents Hamilton-Poisson formulations, integrable deformations, and analyzes the case of Kolmogorov systems. The three-dimensional Lotka-Volterra system with constant population is studied from standard and nonstandard Poisson geometry perspectives.