Integrability of a Family of Four-Dimensional Quadratic Lotka–Volterra Complex Systems
Abstract
This work addresses the integrability of four-dimensional quadratic Lotka–Volterra systems exhibiting (1:−1:i:−i) resonance by identifying the parameter constraints required for such properties to exist. Our results show that, within this family, integrability is connected to linearizability and time-reversibility. To establish these results, we combine theoretical and computational methods. On the theoretical side, we use Poincaré–Dulac normal form theory and methods based on Gröbner basis theory. On the computational side, we apply the algorithms described in the paper to compute normal forms and minimal associated prime ideals required for the analysis of the integrability conditions.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Polynomial and algebraic computation
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Axioms
- Publisher
- MDPI AG
- Volume
- 15
- Issue
- 4
- Pages
- 297–297
- Publication date
- 17 April 2026
- Language
- EN