Darboux first integral conditions and integrability of the 3D Lotka-Volterra system

Abstract

We apply the Darboux theory of integrability to polynomial ODE's of dimension 3. Using this theory and computer algebra, we study the existence of first integrals for the 3-dimensional Lotka-Volterra systems with polynomial invariant algebraic solutions linear and quadratic and determine numerous cases of integrability.

References in corpus (1)

• Deformations of dispersionless KdV hierarchies

Cited by in corpus (9)

• On the complete integrability and linearization of nonlinear ordinary differential equations - Part III: Coupled first order equations
• Nonassociativity and Integrable Hierarchies
• The Integration of Three-Dimensional Lotka-Volterra Systems
• Deformations of dispersionless KdV hierarchies
• Lagrangian structures, integrability and chaos for 3D dynamical equations
• An integrating factor matrix method to find first integrals
• Global dynamics of a family of 3D Lotka-Volterra Systems
• Local Integrability and Linearizability of Three-dimensional Lotka-Volterra Systems
• Integrability and linearizability conditions for a cubic Lotka-Volterra systems