6 papers
Liouvillian integrability of vector fields in higher dimensions
Waleed Aziz, Colin Christopher, Chara Pantazi +1
We consider complex rational vector fields in dimension (equivalently, differential forms of degree in variables) which admit a Liouvillian first integral. Extendin…
Liouvillian integrability of three dimensional vector fields
Waleed Aziz, Colin Christopher, Chara Pantazi +1
We consider a three dimensional complex polynomial, or rational, vector field (equivalently, a two-form in three variables) which admits a Liouvillian first integral. We prove that…
Integrability of a Family of Lotka--Volterra Three Species Biological System
Aween Karim, Azad Amen, Waleed Aziz
The aim of this study is to analyze the integrability problem of Lotka--Volterra three species biological system. The system which considered in this work is a biological plausibil…
Integral Aspects of Resonance Lotka--Volterra Equations with Nonstandard Analysis
Chiman Qadir, Waleed Aziz, Ibrahim Hamad
In this paper the problems of integrable and linearizable Lotka-Volterra equations with -resonance are studied. The necessary conditions for both problems are obtained…
Integrability and linearizability conditions for a cubic Lotka-Volterra systems
Hersh M. Saber, Waleed H. Aziz
The main objective of this work is to investigate the integrability and linearizability problems around a singular point at the origin of the family of differential systems Particu…
Local Integrability and Linearizability of Three-dimensional Lotka-Volterra Systems
Waleed Aziz, Colin Christopher
We investigate the local integrability and linearizability of three dimensional Lotka-Volterra equations at the origin. Necessary and sufficient conditions for both integrability a…