Algebraic independence of the solutions of the classical Lotka-Volterra system
Abstract
Let ( x 1 , y 1 ) , … , ( x n , y n ) be distinct non-constant and non-degenerate solutions of the classical Lotka-Volterra system x ′ = a x y + b x y ′ = c x y + d y where a , b , c , d ∈ C ∖ { 0 } . We show that if d and b are linearly independent over Q , then the solutions are algebraically independent over C , that is t r . d e g C C ( x 1 , y 1 , … , x n , y n ) = 2 n . As a main part of the proof, we show that the set defined by the system in universal differential fields, with d and b linearly independent over Q , is strongly minimal and geometrically trivial. Our techniques also allows us to obtain partial results for some of the more general 2 d -Lotka-Volterra system.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Nonlinear Waves and Solitons
Mathematical and Theoretical Epidemiology and Ecology Models
Publication details
- Journal / source
- Annals of Pure and Applied Logic
- Volume
- 177
- Issue
- 5
- Pages
- 103707–103707
- Publication date
- 2 January 2026
- Language
- EN