Document Type : Research Article
Authors
1
Department of Mathematics, Faculty of Education, Soran University, Erbil-Soran, Iraq
2
- Department of Mathematics, College of Basic Education, Salahaddin University-Erbil, Erbil, Iraq - Department of Mathematics, Basic Education College, Raparin University - Ranya, Iraq - Department of Mathematics, College of Science, Duhok University, Iraq
3
Department of Mathematics, College of Education, Salahaddin University-Erbil, Erbil, Iraq
Abstract
We focus on a chaotic differential system in 3-dimension, including an absolute term and a line of equilibrium points. Which describes as ๐ฅ⁄ = ๐ฆ , ๐ฆ⁄ = −๐๐ฅ + ๐ฆ๐ง , ๐ง⁄ = ๐|๐ฆ| −๐๐ฅ๐ฆ −๐ฅ2 . This system has an implementation by using electronic components. The first purpose of this paper is to provide sufficient conditions for the existence of a limit cycle bifurcating from the zero-Hopf equilibrium point located at the origin of the coordinates. The second aim is to study the integrability of each differential system, one defined in half-space ๐ฆ ≥ 0 and the other in half-space ๐ฆ < 0. We prove that these two systems have no polynomial, rational, or Darboux first integrals for any value of ๐, ๐, and ๐.
Furthermore, we provide a formal series and an analytic first integral of these systems. We also
find Darboux polynomials and exponential factors.
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