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

Shno F. Muhammed; Niazy H. Hussein; Azad I. Amen

doi:10.21271/ZJPAS.32.3.1

Authors

Shno F. Muhammed Department of mathematics, College of Education-Shaqlawa, Salahaddin University-Erbil, Kurdistan Region, Iraq.
Niazy H. Hussein Department of mathematics, Faculty of Science, University of Soran, Erbil, Kurdistan Region, Iraq.
Azad I. Amen 3Department of mathematics, College of Basic Education, Salahaddin University-Erbil, Kurdistan Region, Iraq. *Department of Pathological analysis, College of Science, Knowledge University.

DOI:

https://doi.org/10.21271/ZJPAS.32.3.1

Keywords:

Invariant Algebraic Surfaces, Darboux First Integral, Exponential Factor, Analytic First Integral

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 .

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