Frequency Domain Approach for Hopf Bifurcation Analysis in a Single Mode Laser Model with Time Delay | Zendy

Changjin Xu | Zendy; Maoxin Liao | Zendy

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Frequency Domain Approach for Hopf Bifurcation Analysis in a Single Mode Laser Model with Time Delay

Author(s) -

Changjin Xu,

Maoxin Liao

Publication year - 2010

Publication title -

journal of mathematics research

Language(s) - English

Resource type - Journals

eISSN - 1916-9809

pISSN - 1916-9795

DOI - 10.5539/jmr.v2n3p144

Subject(s) - hopf bifurcation , mathematics , bifurcation , period doubling bifurcation , biological applications of bifurcation theory , transcritical bifurcation , saddle node bifurcation , bifurcation diagram , domain (mathematical analysis) , mathematical analysis , control theory (sociology) , mode (computer interface) , time domain , frequency domain , nonlinear system , physics , computer science , artificial intelligence , control (management) , quantum mechanics , computer vision , operating system

IIn this paper, using frequency domain approach, a single mode laser model with delay is investigated. By choosing the delay ? as a bifurcation parameter, we show that Hopf bifurcation can occur when ? 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 simulations are given to justify the theoretical analysis results. The approach used in this paper is an excellent supplement of previous known ones of Hopf bifurcation analysis

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