Limit cycles and Integrability of a class of 3-dimension chaotic systems

Articles in Press

Document Type : 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

10.24200/sci.2025.64386.8917

Abstract

We focus on a chaotic differential system in 3-dimension, including an absolute term and a line of equilibrium points. Which describes as ๐‘ฅ⁄ = ๐‘ฆ , ๐‘ฆ⁄ = −๐‘Ž๐‘ฅ + ๐‘ฆ๐‘ง , ๐‘ง⁄ = ๐‘|๐‘ฆ| −๐‘๐‘ฅ๐‘ฆ −๐‘ฅ2 . 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 ๐‘ฆ ≥ 0 and the other in half-space ๐‘ฆ < 0. We prove that these two systems have no polynomial, rational, or Darboux first integrals for any value of ๐‘Ž, 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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Main Subjects

Scientia Iranica

Articles in Press, Accepted Manuscript
Available Online from 20 January 2025

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History

  • Receive Date: 14 April 2024
  • Revise Date: 03 November 2024
  • Accept Date: 20 January 2025

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