系統(tǒng)動力學行為復雜性的計算機輔助判定.pdf

1、華中科技大學博士學位論文系統(tǒng)動力學行為復雜性的計算機輔助判定姓名：黃艷申請學位級別：博士專業(yè)：系統(tǒng)分析與集成指導教師：楊曉松20061024華中科技大學博士學位論文IIAbstractIndertostudythecomplexdynamicalbehaviofthesystemwhichcannotbestudiedbyanalyzingmethodthispaperdevelopstheiesmethodsofcomputerass

2、istedverification.Thecomputerassistedverificationofdynamicalbehaviisanewmethodtocombinecomputeralgithmwithprofoundmathematicstheieswhichisaverydifficultjob.Thechaoticityverificationisahardproblemsinceitneedsnotonlydeeply

3、dynamicaltheiesbutalsoagreatdealofnumericalcalculationcomputersimulationaswellasalgithmanalysis.Indertostudythechaoticityofdynamicalsystemthetheyoftopologicalhseshoeisintroducedthenseriesofalgithmsfcomputerassistedverifi

4、cationbasedonthetheyoftopologicalhseshoeareputfwardappliedtothestudyofchemicalsystemsneuralwksystems.Algithmscrespondingstepsaregivenfcomputerassistedverification.Methodsffindinghseshoeinsinglescrollchaoticattractdoubles

5、crollchaoticattractmultiscrollchaoticattractaredescribedrespectively.Furthermebasedonthediscoveryofhseshoeaquantificationaldeionofcomplexityofthesystemcanbegiven.Fthesakeofinvestigatingthedynamicseffectivelythispaperstud

6、iesthealgithmf(un)stablemanifoldofdynamicsbringsfwardtwonewalgithms.Newalgithmsareeconomicalhaveanerrdeduction.BasedontheabovetheiesalgithmsthispaperanalyzesseveralmodelsofHopfieldneuralwksystemsCelluarneuralwksystemsche

7、micaldynamicalsystems.ThispaperstudiesthesesystemsbycomputersimulationLyapunovexponentcalculationcomputerassistedverificationsoon.Richdynamicalbehavisarefoundsuchaschaoshyperchaoslimitcycletwotussoon.Inthispapertwotusphe

8、nomenaarediscoveredinfourdimensionalHopfieldneuralwkstwotusphenomenaarediscoveredinfourdimensionalCellularneuralwks.Furthermecomputerassistedverificationsofexistenceoftwotiaregiveninthispaper.Atthesametimeverificationsof

9、chaoticityofseveralchaoticsystemsaregivenbythecombinationoftopologicalhseshoetheycomputerassistedverification.UsingPoincarsectionPoincarmapthispapergivesaneffectiveverificationftheexistenceoflimitcyclestheexistenceofattr