The general solutions of many three-dimensional Lotka–Volterra systems, previously known
to be at least partially integrable, are constructed with the aid of special functions. Examples …

This paper deals with both integrability and linearizability problems of three dimensional
Lotka–Volterra systems at the origin with rank-2. We give necessary conditions of a system …

We consider a three-dimensional vector field with quadratic nonlinearities and in general
none of the axis plane is invariant. For our investigation, we are interesting in the case of …

We propose an approach for the qualitative investigation of polynomial systems of ODEs
based on algorithms of computational commutative algebra. It can be applied to study …

We study limit cycle bifurcations in a three-dimensional Lotka–Volterra system which models
a food web of three species, one of which is an omnivore. First, using a new approach based …

We study the local integrability at the origin of a nine-parameter family of three-dimensional
Lotka–Volterra differential systems with (3:− 1: 2)-resonance. We give necessary and …

Lotka-Volterra model is one of the most popular in biochemistry. It is used to analyze
cooperativity, autocatalysis, synchronization at large scale and especially oscillatory …

This paper is devoted to investigate the integrability and linearizability problems around a
singular point at the origin of a cubic three-dimensional Lotka-Volterra differential system …