曹克非，男，1963年11月生于云南省昆明市，教授（二级岗），博士生导师，云南省中青年学术和技术带头人。任《云南大学学报（自然科学版）》编委。现在云南大学物理与天文学院物理系、非线性复杂系统中心工作，主要从事复杂网络、非线性复杂系统、混沌、普适性、符号动力学和分形等方面的研究。曾作为青年成员承担完成国家“九五”攀登计划非线性科学项目子课题，承担完成“十五”国家重点基础研究发展规划（“973”计划）非线性科学项目子课题；主持完成国家自然科学基金项目、教育部高等学校博士学科点专项科研基金项目、云南省自然科学基金项目；并作为主要成员参加过多项国家自然科学基金项目、云南省级重点和面上项目以及云南省政府省院省校合作项目。在美国、英国、荷兰、法国、德国、新加坡等出版的国际物理学期刊上发表了多篇论文。
研究工作经历

1997/05–，云南大学物理系、非线性复杂系统中心，教授

1983/09–1997/05，云南民族学院物理系，助教、讲师（1990/07）、副教授（1992/12）、教授（1996/10）

1993/09–1995/04，英国利兹大学生理系、非线性研究中心，访问学者
获奖情况

1.2000年度云南省科学技术奖自然科学类一等奖（一维多符号动力学中的星花积，排名第二，2001/09）

2.云南省有突出贡献的优秀专业技术人才二等奖（2000/10）

3.首届云南省自然科学奖一等奖（非线性符号动力学与超费根鲍姆普适性，排名第二，1996/05）

4.国务院政府特殊津贴（1993/10–）
承担的主要科研项目（主持）

1.国家自然科学基金项目（分形网络系统的几何动力学分析，11365023，2014–2017，在研）

2.国家自然科学基金项目（符号动力学中的非规范星花积与新型超收敛普适性，10565004，2006–2008，已结题）

3.教育部高等学校博士学科点专项科研基金项目（非线性复杂系统中的特征量及相互关系分析，20050673001，2006–2008，已结题）

4.国家重点基础研究发展规划（“973”计划）“非线性科学中的若干前沿问题”项目子课题（符号序列的复杂性分析：符号序列的复杂性与新度量普适性分析，任复杂性课题组副组长，G2000077308，2000–2005，已结题）

5.国家“九五”攀登计划“非线性科学”项目子课题（符号序列分析，青年成员，1999–2000，已结题）

6.云南省自然科学基金项目（非线性物理系统混沌现象的热力学形式与普适性研究，97A007G，1997–2000，已结题）
发表的部分科研论文

1.M.Xu,C.-Y.Xu,H.Wang,Y.-K.Li,J.-B.HuandK.-F.Cao*,Globalandpartitionedreconstructionsofundirectedcomplexnetworks,Eur.Phys.J.B89,55(2016).

2.H.Wang,J.-B.Hu,C.-Y.Xu,D.-H.Zhang,Q.Yan,M.Xu,K.-F.Cao*andX.-S.Zhang,Apathway-basednetworkanalysisofhypertension-relatedgenes,PhysicaA444,928-939(2016);447,569-570(2016).

3.M.Xu,C.-Y.Xu,H.Wang,C.-Z.DengandK.-F.Cao*,Analyticalcontrollabilityofdeterministicscale-freenetworksandCayleytrees,Eur.Phys.J.B88,168(2015).

4.X.-S.Zhang*andK.-F.Cao,Theimpactofcoinfectionsandtheirsimultaneoustransmissiononantigenicdiversityandepidemiccyclingofinfectiousdiseases,BioMedRes.Int.2014,ArticleID375862,23pages(2014).

5.C.-Y.Xu,H.Wang,K.-F.Cao*andS.-L.Peng,Asuperconvergentuniversalityinducedbynon-associativity,Phys.Lett.A378,1505-1509(2014).

6.H.Wang,C.-Y.Xu,J.-B.HuandK.-F.Cao*,Acomplexnetworkanalysisofhypertension-relatedgenes,PhysicaA394,166-176(2014).

7.W.Gao,C.-Y.Xu,S.-L.Peng,andK.-F.Cao*,Universalformofrenormalizableknotsinsymbolicdynamicsofbimodalmaps,Int.J.BifurcationandChaos23,1350160(2013).

8.Q.Liu,K.-F.Cao*,andS.-L.Peng,AgeneralizedKolmogorov-Sinai-likeentropyunderMarkovshiftsinsymbolicdynamics,PhysicaA388,4333-4344(2009).

9.Z.Zhou*,K.-F.Cao,andS.-L.Peng,Newuniversalbifurcationscenarioinone-dimensionaltrimodalmaps,Phys.Lett.A372,3407-3414(2008).

10.W.-B.Zhai,X.-Z.Chen,andK.-F.Cao*,Globalmultifractalrelationbetweentopologicalentropiesandfractaldimensions,Chaos,Solitons&Fractals23,511-518(2005).

11.K.-F.Cao,C.Zhang,andS.-L.Peng,Topologicalentropy,knotsandstarproducts,TheProceedingsofthe14thEuropeanConferenceonIterationTheory(ECIT2002,Évora,Portugal,1-7September2002),editedbyJ.SousaRamos,D.Gronau,C.Mira,L.Reich,A.Sharkovsky,GrazerMath.Ber.346,61-72(2004).

12.Y.-Y.ZhangandK.-F.Cao*,Metricuniversalitiesandsystemsofrenormalizationgroupequationsforbimodalmaps,Chaos,Solitons&Fractals21,457-471(2004).

13.K.-F.CaoandS.-L.Peng*,Homologyofvertexandedgeshiftmatricesinsymbolicdynamicsandentropyinvariants,Int.J.Mod.Phys.B17,4308-4315(2003).

14.K.-F.Cao*,X.-S.Zhang,Z.Zhou,andS.-L.Peng,Devil’scarpetoftopologicalentropyandcomplexityofglobaldynamicalbehavior,Chaos,Solitons&Fractals16,709-726(2003).

15.Z.Zhou*andK.-F.Cao,Aneffectivenumericalmethodoftheword-liftingtechniqueinone-dimensionalmultimodalmaps,Phys.Lett.A310,52-59(2003).

16.K.-F.Cao*,Z.Zhou,W.Gao,andS.-L.Peng,Generalformofsuperuniversalityforfractaldimensionsinone-dimensionalmaps,Int.J.Mod.Phys.B15,4183-4197(2001).

17.K.-F.CaoandS.-L.Peng,Complexityofroutestochaosandglobalregularityoffractaldimensionsinbimodalmaps,Phys.Rev.E60,2745-2760(1999).

18.S.-L.Peng,X.-S.Zhang,andK.-F.Cao,Dualstarproductsandmetricuniversalityinsymbolicdynamicsofthreeletters,Phys.Lett.A246,87-96(1998).

19.S.-L.PengandK.-F.Cao,Globalscalingbehaviorsandchaoticmeasurecharacterizedbytheconvergentratesofperiod-p-tuplingbifurcations,Phys.Rev.E54,3211-3220(1996).

20.J.-X.Shi,K.-F.Cao,T.-L.GuoandS.-L.Peng,Metricuniversalityforthedevil’sstaircaseoftopologicalentropy,Phys.Lett.A211,25-28(1996).

21.K.-F.Cao,Z.-X.Chen,andS.-L.Peng,Globalmetricregularityofthedevil’sstaircaseoftopologicalentropy,Phys.Rev.E51,1989-1995(1995).

22.Z.-X.Chen,K.-F.Cao,andS.-L.Peng,Symbolicdynamicsanalysisoftopologicalentropyanditsmultifractalstructure,Phys.Rev.E51,1983-1988(1995).

23.S.-L.Peng,K.-F.Cao,andZ.-X.Chen,Devil’sstaircaseoftopologicalentropyandglobalmetricregularity,Phys.Lett.A193,437-443(1994);196,378(1995).

24.K.-F.CaoandS.-L.Peng,Universalscalingofgeneralizeddimensionsoncriticalstrangesets,J.Phys.A:Math.Gen.25,589-599(1992).

25.K.-F.Cao,R.-L.Liu,andS.-L.Peng,AnewuniversalityforfractaldimensionsofFeigenbaum-typeattractors,Phys.Lett.A136,213-215(1989).

26.S.-L.PengandK.-F.Cao,Anewglobalregularityoffractaldimensionsoncriticalpointsoftransitionstochaos,Phys.Lett.A131,261-264(1988);133,543(1988).
指导研究生情况

硕士研究生（毕业31人，在读3人）

博士研究生（毕业4人，在读4人）

Ke-FeiCAO,male,bornNovember1963,Kunming,YunnanProvince,China.ProfessoratCenterforNonlinearComplexSystems,DepartmentofPhysics,SchoolofPhysicsandAstronomy,YunnanUniversity;Supervisorofdoctoralstudents;OneoftheYoungandMiddle-AgedAcademic/TechnicalLeadersofYunnanProvince.EditorialBoardmemberofJournalofYunnanUniversity(NaturalSciencesEdition).Researchinterests:ComplexNetworks,NonlinearComplexSystems,Chaos,Universality,SymbolicDynamics,Fractals,andrelatedtopics.ProjectscompletedweresupportedbytheNationalandYunnanProvincialGovernments.SomepaperswerepublishedininternationaljournalsofUSA,UK,TheNetherlands,France,Germany,Singapore,etc.
ResearchExperienceandAppointments

1997/05–,Professor,CenterforNonlinearComplexSystems,DepartmentofPhysics,YunnanUniversity

1983/09–1997/05,TeachingAssistant,Lecturer(1990/07),AssociateProfessor(1992/12),Professor(1996/10),DepartmentofPhysics,YunnanInstituteoftheNationalities

1993/09–1995/04,VisitingScholar,DepartmentofPhysiologyandCentreforNonlinearStudies,UniversityofLeeds,UK
AwardsandHonors

1.TheFirstPrize,TheNaturalScienceAwardsofthe2000ScienceandTechnologyAwardsofYunnanProvince(StarProductsinOne-DimensionalMulti-SymbolicDynamics,2001/09)

2.TheSecondPrize,TheExcellentProfessionalandTechnicalTalentswithOutstandingContributionsofYunnanProvince(2000/10)

3.TheFirstPrize,TheNaturalScienceAwardsofYunnanProvince(NonlinearSymbolicDynamicsandGlobalFeigenbaumSuper-Universality,1996/05)

4.TheGovernmentSpecialAllowancebytheStateCouncilofP.R.China(1993/10–)
SelectedResearchProjects

1.ProjectsupportedbytheNationalNaturalScienceFoundationofChina(NSFC):Influenceofgeometryondynamicsinfractalnetworksystems,GrantNo.11365023,2014–2017

2.ProjectsupportedbytheNationalNaturalScienceFoundationofChina(NSFC):Non-normalstarproductsandnewsuper-convergentuniversalityinsymbolicdynamics,GrantNo.10565004,2006–2008

3.ProjectsupportedbytheSpecializedResearchFundfortheDoctoralProgramofHigherEducationofChina(SRFDP):Analysesofcharacteristicquantitiesandtheirrelationshipsinnonlinearcomplexsystems,GrantNo.20050673001,2006–2008)

4.Sub-projectsupportedbytheSpecialFundsforMajorStateBasicResearchProjectsofChina(the‘‘973’’Program):Someimportantproblemsinnonlinearscience(Complexityanalysisofsymbolicsequences:Complexityofsymbolicsequencesandnewmetricuniversality),GrantNo.G2000077308,2000–2005

5.Sub-projectsupportedbytheNationalKeyProjectforFundamentalResearch(theClimbingProgram):NonlinearScience(Analysisofsymbolicsequences),1999–2000

6.ProjectsupportedbytheNaturalScienceFoundationofYunnanProvince:Theresearchonthermodynamicformalismanduniversalityofchaoticphenomenainnonlinearphysicalsystems,GrantNo.97A007G,1997–2000
SelectedPublications

1.M.Xu,C.-Y.Xu,H.Wang,Y.-K.Li,J.-B.HuandK.-F.Cao*,Globalandpartitionedreconstructionsofundirectedcomplexnetworks,Eur.Phys.J.B89,55(2016).

2.H.Wang,J.-B.Hu,C.-Y.Xu,D.-H.Zhang,Q.Yan,M.Xu,K.-F.Cao*andX.-S.Zhang,Apathway-basednetworkanalysisofhypertension-relatedgenes,PhysicaA444,928-939(2016);447,569-570(2016).

3.M.Xu,C.-Y.Xu,H.Wang,C.-Z.DengandK.-F.Cao*,Analyticalcontrollabilityofdeterministicscale-freenetworksandCayleytrees,Eur.Phys.J.B88,168(2015).

4.X.-S.Zhang*andK.-F.Cao,Theimpactofcoinfectionsandtheirsimultaneoustransmissiononantigenicdiversityandepidemiccyclingofinfectiousdiseases,BioMedRes.Int.2014,ArticleID375862,23pages(2014).

5.C.-Y.Xu,H.Wang,K.-F.Cao*andS.-L.Peng,Asuperconvergentuniversalityinducedbynon-associativity,Phys.Lett.A378,1505-1509(2014).

6.H.Wang,C.-Y.Xu,J.-B.HuandK.-F.Cao*,Acomplexnetworkanalysisofhypertension-relatedgenes,PhysicaA394,166-176(2014).

7.W.Gao,C.-Y.Xu,S.-L.Peng,andK.-F.Cao*,Universalformofrenormalizableknotsinsymbolicdynamicsofbimodalmaps,Int.J.BifurcationandChaos23,1350160(2013).

8.Q.Liu,K.-F.Cao*,andS.-L.Peng,AgeneralizedKolmogorov-Sinai-likeentropyunderMarkovshiftsinsymbolicdynamics,PhysicaA388,4333-4344(2009).

9.Z.Zhou*,K.-F.Cao,andS.-L.Peng,Newuniversalbifurcationscenarioinone-dimensionaltrimodalmaps,Phys.Lett.A372,3407-3414(2008).

10.W.-B.Zhai,X.-Z.Chen,andK.-F.Cao*,Globalmultifractalrelationbetweentopologicalentropiesandfractaldimensions,Chaos,Solitons&Fractals23,511-518(2005).

11.K.-F.Cao,C.Zhang,andS.-L.Peng,Topologicalentropy,knotsandstarproducts,TheProceedingsofthe14thEuropeanConferenceonIterationTheory(ECIT2002,Évora,Portugal,1-7September2002),editedbyJ.SousaRamos,D.Gronau,C.Mira,L.Reich,A.Sharkovsky,GrazerMath.Ber.346,61-72(2004).

12.Y.-Y.ZhangandK.-F.Cao*,Metricuniversalitiesandsystemsofrenormalizationgroupequationsforbimodalmaps,Chaos,Solitons&Fractals21,457-471(2004).

13.K.-F.CaoandS.-L.Peng*,Homologyofvertexandedgeshiftmatricesinsymbolicdynamicsandentropyinvariants,Int.J.Mod.Phys.B17,4308-4315(2003).

14.K.-F.Cao*,X.-S.Zhang,Z.Zhou,andS.-L.Peng,Devil’scarpetoftopologicalentropyandcomplexityofglobaldynamicalbehavior,Chaos,Solitons&Fractals16,709-726(2003).

15.Z.Zhou*andK.-F.Cao,Aneffectivenumericalmethodoftheword-liftingtechniqueinone-dimensionalmultimodalmaps,Phys.Lett.A310,52-59(2003).

16.K.-F.Cao*,Z.Zhou,W.Gao,andS.-L.Peng,Generalformofsuperuniversalityforfractaldimensionsinone-dimensionalmaps,Int.J.Mod.Phys.B15,4183-4197(2001).

17.K.-F.CaoandS.-L.Peng,Complexityofroutestochaosandglobalregularityoffractaldimensionsinbimodalmaps,Phys.Rev.E60,2745-2760(1999).

18.S.-L.Peng,X.-S.Zhang,andK.-F.Cao,Dualstarproductsandmetricuniversalityinsymbolicdynamicsofthreeletters,Phys.Lett.A246,87-96(1998).

19.S.-L.PengandK.-F.Cao,Globalscalingbehaviorsandchaoticmeasurecharacterizedbytheconvergentratesofperiod-p-tuplingbifurcations,Phys.Rev.E54,3211-3220(1996).

20.J.-X.Shi,K.-F.Cao,T.-L.GuoandS.-L.Peng,Metricuniversalityforthedevil’sstaircaseoftopologicalentropy,Phys.Lett.A211,25-28(1996).

21.K.-F.Cao,Z.-X.Chen,andS.-L.Peng,Globalmetricregularityofthedevil’sstaircaseoftopologicalentropy,Phys.Rev.E51,1989-1995(1995).

22.Z.-X.Chen,K.-F.Cao,andS.-L.Peng,Symbolicdynamicsanalysisoftopologicalentropyanditsmultifractalstructure,Phys.Rev.E51,1983-1988(1995).

23.S.-L.Peng,K.-F.Cao,andZ.-X.Chen,Devil’sstaircaseoftopologicalentropyandglobalmetricregularity,Phys.Lett.A193,437-443(1994);196,378(1995).

24.K.-F.CaoandS.-L.Peng,Universalscalingofgeneralizeddimensionsoncriticalstrangesets,J.Phys.A:Math.Gen.25,589-599(1992).

25.K.-F.Cao,R.-L.Liu,andS.-L.Peng,AnewuniversalityforfractaldimensionsofFeigenbaum-typeattractors,Phys.Lett.A136,213-215(1989).

26.S.-L.PengandK.-F.Cao,Anewglobalregularityoffractaldimensionsoncriticalpointsoftransitionstochaos,Phys.Lett.A131,261-264(1988);133,543(1988).
SupervisionofMaster'sandDoctoralStudents

Master'sstudents(graduated:31;training:3)

Doctoralstudents(graduated:4;training:4)