Darboux and Analytic First Integrals of Kingni–Jafari System with Only One Stable Equilibrium Point.

Abstract

In this paper, we illustrate by an evidence that the Kingni–Jafari differential system where and are real parameters has no Darboux and rational first integrals for any value of Furthermore, we show that this system has no global first integrals for and . Also, an analytic first integral for some generic condition is studied of this system at the neighborhood of the equilibrium point .