Bifurcation phenomena and control analysis in class-B laser system with delayed feedback

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• 作者：Hongbin Wang (1)
  Weihua Jiang (1)
  Yuting Ding (2)
  
  1. Department of Mathematics ; Harbin Institute of Technology ; Harbin ; 150001 ; China
  2. Department of Mathematics ; Northeast Forestry University ; Harbin ; 150040 ; China
  
• 关键词：Class ; B laser system ; Delayed feedback control ; Hopf bifurcation ; Double Hopf bifurcation ; Normal form
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：79
• 期：4
• 页码：2421-2438
• 全文大小：1,308 KB
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• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

In this paper, we study dynamics in delayed class-B laser system, with particular attention focused on Hopf and double Hopf bifurcations. Firstly, we identify the critical values for stability switches, Hopf and double Hopf bifurcations and derive the normal forms near the Hopf and double Hopf bifurcations critical points. By analyzing local dynamics near bifurcation critical points, we show how the delayed feedback control parameters effect the dynamical behaviors of the system. Furthermore, detailed numerical analysis using MATLAB extends the local bifurcation analysis to a global picture, and stable windows are observed as we change control parameter. Namely, even for parameter values not chosen in the neighborhood of the Hopf bifurcation critical points, two families of stable periodic solutions, which are resulted from Hopf bifurcation, exist in a large region of delay, and they merge into a family of stable and globally existed periodic solutions. Finally, by choosing proper control parameters, numerical simulations, including stable equilibrium, stable periodic solutions and stable quasiperiodic solutions are presented to demonstrate the theoretical results. Therefore, in accordance with above theoretical analysis, reasonable lasers with proper control parameters can be designed in order to achieve various applications.