２０２３年７月四川大学学报(自然科学版)Jul．２０２３第６０卷第４期JournalofSichuanUniversity(NaturalScienceEdition)Vol．６０No．４含相关色噪声和周期方波信号的双稳系统的随机共振曾小玲１,任芮彬２,邓科１(１．四川大学数学学院,成都６１００６４;２．西南交通大学数学学院,成都６１１７５６)摘要:本文研究了含相关色噪声和周期方波信号的双稳系统的随机共振(SR)．在绝热极限条件下,本文利用统一色噪声逼近(UCNA)法将原系统转化为相关高斯白噪声驱动的新双稳系统,给出其FokkerＧPlanck方程后基于双态理论推导了系统信噪比(SNR)的表达式．本文分析了势参数、噪声参数及外力参数对信噪比的影响,发现对所有参数随机共振均出现．本研究可望为实际应用提供理论基础．关键词:随机共振;相关色噪声;周期方波信号;双稳系统中图分类号:O２９文献标识码:ADOI:１０．１９９０７/j．０４９０Ｇ６７５６．２０２３．０４１００３收稿日期:２０２２Ｇ０９Ｇ１７基金项目:国家重点研发计划(２０２０YFA０７１４０００)作者简介:曾小玲(１９９８－),女,重庆万州人,硕士研究生,主要研究方向为非线性动力系统．EＧmail:２６３９８１９２３０＠qq．com通讯作者:邓科．EＧmail:dk_８３＠１２６．comStochasticresonanceinabistablesystemwithcorrelatedcolorednoisesandperiodicsquarewavesignalZENGXiaoＧLing１,RENRuiＧBin２,DENGKe１(１．SchoolofMathematics,SichuanUniversity,Chengdu６１００６４,China;２．CollegeofMathematics,SouthwestJiaotongUniversity,Chengdu６１１７５６,China)Abstract:Stochasticresonance(SR)inabistablesystemwithcorrelatedcolorednoisesandperiodicsquarewavesignalisexplored．Giventheadiabaticlimitcondition,theoriginalsystemistransformedintoanewbistablesystemdrivenbycorrelatedwhiteGaussiannoisesbyusingtheunifiedcolorednoiseapproximation(UCNA)method．ThentheFokkerＧPlanckequationisgivenforthenewsystemandexＧactexpressionforthesignalＧtoＧnoiseratio(SNR)isdeducedbyvirtueofthetwoＧstatetheory．Finally,dependenceofSNRonthesystemparameters,includingthepotenialparamaters,thenoiseparametersandtheexternalforceparameters,isanalized．ItisshownthatSRappearsforallparameters．TheobＧtainedresultsareexpectedtoprovideatheoreticalbasisforpracticalapplications．Keywords:SR;Corr...
