Theory Of Stability And Bifurcation In A Multi-quantum Well Laserwith Opto-electronic Delayed Fedback

In recent years, the semiconductorlaserhas become the focusin thecurrentchaoticdynamics with itspotential applications in chaoticoptical communication.Itseemsmore importantto studythe semiconductorlasersystem, whichcan generatechaoticoptical pulses andother dynamicphenomena.Thechaotic characteristicsofthe systemshas been widelysuggested by many expertsto applyto securityandsecrecywork,andinfields of engineering sciencesand experimental sciences,theoptical feedbackMQW laseris still of great values.Thispaper mainlyanalyzesthe local stabilityof theequilibriumpoint andHopfbifurcation issues of a classof delayed feedback photoelectricMQW lasers withthe varyingof delay.Main work is as follows:Firstly, obtainthecharacteristic equationby linearizingthe equations.Then,obtainthe existenceconditions of asymptoticallystable andHopf bifurcationbyanalyzingthe distributionof eigenvalues.And research into some possibleresults ofthe stabilitygenerated by the varyof thedelay.Secondly,on the conditionof theexistence of the bifurcation, pan theequilibriumpoint tothe origin,usingthe centermanifold theory andnormalformmethodtoget thecomputational formulawhichcan decide thestability andHopfbifurcation direction.Finally,in orderto support thetheoretical findingsbetter, we applyMatlabsoftwaretodoing thenumerical simulation.