¹Guizhou Key Laboratory of Economics System Simulation, Guizhou College of Finance and Economics, Guiyang 550004, P.R. China
²Department of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, P.R. China

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Abstract—In this paper, the dynamic behavior of a single mode laser model with delay is investigated via frequency domain approach. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur when τ passes a sequence of critical values. This means that a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulation results are consistent with the theoretical ones. The approach used in this paper is an excellent supplement of previous known ones of Hopf bifurcation analysis.

Index Terms—Single mode laser model, Hopf bifurcation, stability, frequency domain approach, Nyquist criterion.

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Cite: Changjin Xua, Peiluan Li, "Bifurcations for A Single Mode Laser Model with Time Delay in Frequency Domain Methods," Journal of Computers vol. 7, no. 8, pp. 1825-1830, 2012.