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Multimachine Stability01:25

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Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
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Instability in optical injection locking semiconductors lasers using multiparametric bifurcation analysis.

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  • 1Department of Basic Scientific Education, Higher Technical Teachers Training College, University of Ebolowa, PO Box 886, Ebolowa, Cameroon.

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This study explores complex dynamics in semiconductor lasers (SCLs) under optical injection, revealing new bifurcation behaviors and chaotic phenomena. Findings highlight critical parameter effects on laser stability and locking dynamics.

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Area of Science:

  • Nonlinear Dynamics
  • Semiconductor Laser Physics
  • Optical Engineering

Background:

  • Semiconductor lasers (SCLs) exhibit complex dynamics under optical injection.
  • Understanding bifurcations is crucial for controlling SCL behavior.

Purpose of the Study:

  • Investigate bifurcations of equilibria and transients in SCLs with optical injection.
  • Analyze two- and three-parameter bifurcations and their impact on laser dynamics.
  • Characterize chaotic phenomena and develop methods for their quantification.

Main Methods:

  • Modified rate equations for SCLs.
  • Analytical and numerical multiparametric bifurcation analysis.
  • 3D-plots and projections for visualizing dynamics.
  • Investigation of transient regimes and Lyapunov exponents.

Main Results:

  • Demonstrated Bogdanov-Takens and Gavrilov-Guckenheimer bifurcations.
  • Identified a zero frequency detuning well near Hopf bifurcations.
  • Revealed rich locking dynamics, including cusp bifurcations and multi-equilibrium regions.
  • Characterized bursting, metastable chaos, and complex attractors.
  • Showcased zero α-factor effects on unlocking regions and Hopf bifurcations.

Conclusions:

  • Optical injection induces diverse and complex dynamical behaviors in SCLs.
  • Bifurcation analysis provides critical insights into SCL stability and control.
  • The study proposes novel methods for quantifying complex dynamics and attractors.