简介：Thispaperstudiesastochasticallyforcedchemostatmodelwithfeedbackcontrolinwhichtwoorganismscompeteforasinglegrowth-limitingsubstrate.Inthedeterministiccounterpart,previousresearchesshowthatthecoexistenceoftwocompetingorganismsmaybeachievedasastablepositiveequilibriumorastablepositiveperiodicsolutionbydierentfeedbackschedules.Inthestochasticcase,basedonthestochasticsensitivityfunctiontechnique,weconstructtheconfidencedomainsfordierentfeedbackscheduleswhichallowustofindtheconfigurationalarrangementsofthestochasticattractorsandanalyzethedispersionoftherandomstatesofthestochasticmodel.

简介：Inthispaper,athreedimensionalratio-dependentchemostatmodelwithperiod-icallypulsedinputisconsidered.ByusingthediscretedynamicalsystemdeterminedbythestroboscopicmapandFloquettheorem,anexactperiodicsolutionwithpositiveconcentrationsofsubstrateandpredatorintheabsenceofpreyisobtained.Whenβislessthansomecriti-calvaluetheboundaryperiodicsolution(x_s(t),0,z_s(t))islocallystable,andwhenβislargerthanthecriticalvaluethereareperiodicoscillationsinsubstrate,preyandpredator.IncreasingtheimpulsiveperiodT,thesystemundergoesaseriesofperiod-doublingbifurcationleadingtochaos,whichimpliesthatthedynamicalbehaviorsoftheperiodicallypulsedratio-dependentpredator-preyecosystemareverycomplex.