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Discretization of laser model with bifurcation analysis and chaos control

  • Qamar Din (Departement of Mathematics, University of Poonch Rawalakot) ;
  • Waqas Ishaque (Departement of Mathematics, University of Poonch Rawalakot) ;
  • Iqra Maqsood (Departement of Mathematics, University of Poonch Rawalakot) ;
  • Abdelouahed Tounsi (Department of Civil Engineering, University of Sidi Bel)
  • Received : 2022.10.05
  • Accepted : 2022.12.20
  • Published : 2023.07.25
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Abstract

This paper investigates the dynamics and stability of steady states in a continuous and discrete-time single-mode laser system. By using an explicit criteria we explored the Neimark-Sacker bifurcation of the single mode continuous and discrete-time laser model at its positive equilibrium points. Moreover, we discussed the parametric conditions for the existence of period-doubling bifurcations at their positive steady states for the discrete time system. Both types of bifurcations are verified by the Lyapunov exponents, while the maximum Lyapunov ensures chaotic and complex behaviour. Furthermore, in a three-dimensional discrete-time laser model, we used a hybrid control method to control period-doubling and Neimark-Sacker bifurcation. To validate our theoretical discussion, we provide some numerical simulations.

Keywords

Acknowledgement

The authors thank the main editor and anonymous referees for their valuable comments and suggestions leading to improvement of this paper. This research work was funded by Higher Education Commission (HEC) Pakistan under NRPU Project No. 20-16985/NRPU/R\&D/HEC/2021.

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