Integrability and dynamics Analysis of the Chaos Laser System

Articles in Press

Document Type : Research Article

Author

Department of mathematics, college of basic education-Salahaddin university-Hawler

Abstract

In this article the complex dynamics of a laser model, which externally injected class 𝐵 which is described by a system of three nonlinear ordinary differential equations with two parameters

for field intensity phase and population inversion, are studied. In particular, we investigate the integrability and nonintegrabilty of laser system in three dimension. We prove that system is complete integrable only when the parameters are zero. Particularly, we study polynomial, rational, Darboux and analytic first integrals of the mentioned system. Moreover, we compute all the invariant algebraic surfaces and exponential factors of this system. We find sufficient conditions for the existence of periodic orbits emanating from an equilibrium point origin of a laser differential system with a first integral.

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Scientia Iranica

Articles in Press, Accepted Manuscript
Available Online from 06 December 2025

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History

  • Receive Date: 11 October 2022
  • Revise Date: 11 December 2022
  • Accept Date: 19 April 2023

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