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

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