非光滑与多平衡态下的簇发振荡机理分析

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1、万方数据江苏大学硕士学位论文ABSTRACTNonlineardyn锄icalsystemhasmarlycomplexandInultipledyn枷cbehaviors，becauseofwhichithasbecomeoneofthemostimportantresearchdirectionsinthefieldofscience．Inthisp印er，Ⅱ1enon-smoothdyIl锄icalsystemandDumngeqpationwithtwotimescalesarestudiedtoi11ves

2、tigatet11eirdyn锄icbehaViorsaswellast11emechanism．Firstly，theburstingoscillationsaswenasthernechaIlisminaperiodicallyexcitedpiecewise—linearsystemWitha11orderg印be铆eentheexciting仔equencyandthenatural舶quencyarestudied．BasedonmetypicalChua’scircuit，aperiodicallyexc

3、itedmodelwimaperiodicallych锄gingcurrentsouI．ceisestablished，inwhichthenolllillearcharacteristicsoftheresistorisexpressedi11temsofacontinuousfhnctionwithmultiplepiecewise一1i11e2ursegments．BychoosiIlgsuitablevaluesofpar锄etersandexcited仔equencyandanalyzingthenoIll

4、inalequilibriumorbitsofthe1iIlearsubsystemsindif．ferentregionsdiVidedbymebreakpoints，criticalconditionscorrespondmgtoregularandnon—smoothbi丘Jrcationsarederived．Twotypicalc2usesinwhich吐letr旬ectoriespassacrossdifIferentn咖bersofnon-smoothbound撕esareinvestigated，re

5、sultingi11di圩erentfomsofburstingoscillationsareobtained．Itispointedmatnotonlythepropertiesoftheno面nalequilibriumorbitsindi虢rentregionsbutalsothenon-smoothboundariesmayinnuencetheburstingattractors．Furtllemore，unlikeⅡ1ecoIulectionsbet、Ⅳeenquiescentstates(QSs)and

6、spikjngstates(SPs)Viaregularbi向rcationsinsmoothvectorfields，fortheburstingoscillationsinpiecewise—lillearsystems，thetransitionsbetweenQSsandSPsmaybecausedbynon—smoothbi如rcationsorⅡ1eabruptaltemationsbetweentwodifjEIerentsubsystemsonbothsidesofthenon—smoothbouIl

7、daries．TTT万方数据Secondly，thisp印erinVestigatesdyn锄icalbehaViorsaswellasmemechanismofaDumngequationwithperiodicallypar锄etricexcitation．Theordergapbetweentlleexciting矗equencyandthenatural丹eqUencyleadstothecouplingof俩otimescales．SincenoobViousslowandfastsubsystemeXis

8、ts，themethodofslow-f如ta11alysiscallnotbedirectlyemployedtoapproachthemechanismofthebursting．Byintroducmgthegeneralizedautonomoussystem(GAS)andthetransfomedphaseportraits(TPP