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云南大學物理與天文學院研究生導師介紹：曹克非
曹克非，男，1963年11月生于云南省昆明市，教授（二級崗），博士生導師，云南省中青年學術和技術帶頭人。任《云南大學學報（自然科學版）》編委。現在云南大學物理與天文學院物理系、非線性復雜系統中心工作，主要從事復雜網絡、非線性復雜系統、混沌、普適性、符號動力學和分形等方面的研究。曾作為青年成員承擔完成國家“九五”攀登計劃非線性科學項目子課題，承擔完成“十五”國家重點基礎研究發展規劃（“973”計劃）非線性科學項目子課題；主持完成國家自然科學基金項目、教育部高等學校博士學科點專項科研基金項目、云南省自然科學基金項目；并作為主要成員參加過多項國家自然科學基金項目、云南省級重點和面上項目以及云南省政府省院省校合作項目。在美國、英國、荷蘭、法國、德國、新加坡等出版的國際物理學期刊上發表了多篇論文。
研究工作經歷
1997/05 – ，云南大學物理系、非線性復雜系統中心，教授
1983/09 – 1997/05，云南民族學院物理系，助教、講師（1990/07）、副教授（1992/12）、教授（1996/10）
1993/09 – 1995/04，英國利茲大學生理系、非線性研究中心，訪問學者
獲獎情況
1. 2000年度云南省科學技術獎自然科學類一等獎（一維多符號動力學中的星花積，排名第二，2001/09）
2. 云南省有突出貢獻的優秀專業技術人才二等獎（2000/10）
3. 首屆云南省自然科學獎一等獎（非線性符號動力學與超費根鮑姆普適性，排名第二，1996/05）
4. 國務院政府特殊津貼（1993/10 – ）
承擔的主要科研項目（主持）
1. 國家自然科學基金項目（分形網絡系統的幾何動力學分析，11365023，2014 – 2017，在研）
2. 國家自然科學基金項目（符號動力學中的非規范星花積與新型超收斂普適性，10565004，2006 – 2008，已結題）
3. 教育部高等學校博士學科點專項科研基金項目（非線性復雜系統中的特征量及相互關系分析，20050673001，2006 – 2008，已結題）
4. 國家重點基礎研究發展規劃（“973”計劃）“非線性科學中的若干前沿問題”項目子課題（符號序列的復雜性分析：符號序列的復雜性與新度量普適性分析，任復雜性課題組副組長，G2000077308，2000 – 2005，已結題）
5. 國家“九五”攀登計劃“非線性科學”項目子課題（符號序列分析，青年成員，1999 – 2000，已結題）
6. 云南省自然科學基金項目（非線性物理系統混沌現象的熱力學形式與普適性研究，97A007G，1997 – 2000，已結題）
發表的部分科研論文
1. M. Xu, C.-Y. Xu, H. Wang, Y.-K. Li, J.-B. Hu and K.-F. Cao*, Global and partitioned reconstructions of undirected complex networks, Eur. Phys. J. B 89, 55 (2016).
2. H. Wang, J.-B. Hu, C.-Y. Xu, D.-H. Zhang, Q. Yan, M. Xu, K.-F. Cao* and X.-S. Zhang, A pathway-based network analysis of hypertension-related genes, Physica A 444, 928-939 (2016); 447, 569-570 (2016).
3. M. Xu, C.-Y. Xu, H. Wang, C.-Z. Deng and K.-F. Cao*, Analytical controllability of deterministic scale-free networks and Cayley trees, Eur. Phys. J. B 88, 168 (2015).
4. X.-S. Zhang* and K.-F. Cao, The impact of coinfections and their simultaneous transmission on antigenic diversity and epidemic cycling of infectious diseases, BioMed Res. Int. 2014, Article ID 375862, 23 pages (2014).
5. C.-Y. Xu, H. Wang, K.-F. Cao* and S.-L. Peng, A superconvergent universality induced by non-associativity, Phys. Lett. A 378, 1505-1509 (2014).
6. H. Wang, C.-Y. Xu, J.-B. Hu and K.-F. Cao*, A complex network analysis of hypertension-related genes, Physica A 394, 166-176 (2014).
7. W. Gao, C.-Y. Xu, S.-L. Peng, and K.-F. Cao*, Universal form of renormalizable knots in symbolic dynamics of bimodal maps, Int. J. Bifurcation and Chaos 23, 1350160 (2013).
8. Q. Liu, K.-F. Cao*, and S.-L. Peng, A generalized Kolmogorov-Sinai-like entropy under Markov shifts in symbolic dynamics, Physica A 388, 4333-4344 (2009).
9. Z. Zhou*, K.-F. Cao, and S.-L. Peng, New universal bifurcation scenario in one-dimensional trimodal maps, Phys. Lett. A 372, 3407-3414 (2008).
10. W.-B. Zhai, X.-Z. Chen, and K.-F. Cao*, Global multifractal relation between topological entropies and fractal dimensions, Chaos, Solitons & Fractals 23, 511-518 (2005).
11. K.-F. Cao, C. Zhang, and S.-L. Peng, Topological entropy, knots and star products, The Proceedings of the 14th European Conference on Iteration Theory (ECIT 2002, Évora, Portugal, 1-7 September 2002), edited by J. Sousa Ramos, D. Gronau, C. Mira, L. Reich, A. Sharkovsky, Grazer Math. Ber. 346, 61-72 (2004).
12. Y.-Y. Zhang and K.-F. Cao*, Metric universalities and systems of renormalization group equations for bimodal maps, Chaos, Solitons & Fractals 21, 457-471 (2004).
13. K.-F. Cao and S.-L. Peng*, Homology of vertex and edge shift matrices in symbolic dynamics and entropy invariants, Int. J. Mod. Phys. B 17, 4308-4315 (2003).
14. K.-F. Cao*, X.-S. Zhang, Z. Zhou, and S.-L. Peng, Devil’s carpet of topological entropy and complexity of global dynamical behavior, Chaos, Solitons & Fractals 16, 709-726 (2003).
15. Z. Zhou* and K.-F. Cao, An effective numerical method of the word-lifting technique in one-dimensional multimodal maps, Phys. Lett. A 310, 52-59 (2003).
16. K.-F. Cao*, Z. Zhou, W. Gao, and S.-L. Peng, General form of superuniversality for fractal dimensions in one-dimensional maps, Int. J. Mod. Phys. B 15, 4183-4197 (2001).
17. K.-F. Cao and S.-L. Peng, Complexity of routes to chaos and global regularity of fractal dimensions in bimodal maps, Phys. Rev. E 60, 2745-2760 (1999).
18. S.-L. Peng, X.-S. Zhang, and K.-F. Cao, Dual star products and metric universality in symbolic dynamics of three letters, Phys. Lett. A 246, 87-96 (1998).
19. S.-L. Peng and K.-F. Cao, Global scaling behaviors and chaotic measure characterized by the convergent rates of period-p-tupling bifurcations, Phys. Rev. E 54, 3211-3220 (1996).
20. J.-X. Shi, K.-F. Cao, T.-L. Guo and S.-L. Peng, Metric universality for the devil’s staircase of topological entropy, Phys. Lett. A 211, 25-28 (1996).
21. K.-F. Cao, Z.-X. Chen, and S.-L. Peng, Global metric regularity of the devil’s staircase of topological entropy, Phys. Rev. E 51, 1989-1995 (1995).
22. Z.-X. Chen, K.-F. Cao, and S.-L. Peng, Symbolic dynamics analysis of topological entropy and its multifractal structure, Phys. Rev. E 51, 1983-1988 (1995).
23. S.-L. Peng, K.-F. Cao, and Z.-X. Chen, Devil’s staircase of topological entropy and global metric regularity, Phys. Lett. A 193, 437-443 (1994); 196, 378 (1995).
24. K.-F. Cao and S.-L. Peng, Universal scaling of generalized dimensions on critical strange sets, J. Phys. A: Math. Gen. 25, 589-599 (1992).
25. K.-F. Cao, R.-L. Liu, and S.-L. Peng, A new universality for fractal dimensions of Feigenbaum-type attractors, Phys. Lett. A 136, 213-215 (1989).
26. S.-L. Peng and K.-F. Cao, A new global regularity of fractal dimensions on critical points of transitions to chaos, Phys. Lett. A 131, 261-264 (1988); 133, 543 (1988).
指導研究生情況
碩士研究生（畢業31人，在讀3人）
博士研究生（畢業4人，在讀4人）
Ke-Fei CAO, male, born November 1963, Kunming, Yunnan Province, China. Professor at Center for Nonlinear Complex Systems, Department of Physics, School of Physics and Astronomy, Yunnan University; Supervisor of doctoral students; One of the Young and Middle-Aged Academic/Technical Leaders of Yunnan Province. Editorial Board member of Journal of Yunnan University (Natural Sciences Edition). Research interests: Complex Networks, Nonlinear Complex Systems, Chaos, Universality, Symbolic Dynamics, Fractals, and related topics. Projects completed were supported by the National and Yunnan Provincial Governments. Some papers were published in international journals of USA, UK, The Netherlands, France, Germany, Singapore, etc.
Research Experience and Appointments
1997/05 – , Professor, Center for Nonlinear Complex Systems, Department of Physics, Yunnan University
1983/09 – 1997/05, Teaching Assistant, Lecturer (1990/07), Associate Professor (1992/12), Professor (1996/10), Department of Physics, Yunnan Institute of the Nationalities
1993/09 – 1995/04, Visiting Scholar, Department of Physiology and Centre for Nonlinear Studies, University of Leeds, UK
Awards and Honors
1. The First Prize, The Natural Science Awards of the 2000 Science and Technology Awards of Yunnan Province (Star Products in One-Dimensional Multi-Symbolic Dynamics, 2001/09)
2. The Second Prize, The Excellent Professional and Technical Talents with Outstanding Contributions of Yunnan Province (2000/10)
3. The First Prize, The Natural Science Awards of Yunnan Province (Nonlinear Symbolic Dynamics and Global Feigenbaum Super-Universality, 1996/05)
4. The Government Special Allowance by the State Council of P. R. China (1993/10 – )
Selected Research Projects
1. Project supported by the National Natural Science Foundation of China (NSFC): Influence of geometry on dynamics in fractal network systems, Grant No. 11365023, 2014 – 2017
2. Project supported by the National Natural Science Foundation of China (NSFC): Non-normal star products and new super-convergent universality in symbolic dynamics, Grant No. 10565004, 2006 – 2008
3. Project supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (SRFDP): Analyses of characteristic quantities and their relationships in nonlinear complex systems, Grant No. 20050673001, 2006 – 2008)
4. Sub-project supported by the Special Funds for Major State Basic Research Projects of China (the ‘‘973’’ Program): Some important problems in nonlinear science (Complexity analysis of symbolic sequences: Complexity of symbolic sequences and new metric universality), Grant No. G2000077308, 2000 – 2005
5. Sub-project supported by the National Key Project for Fundamental Research (the Climbing Program): Nonlinear Science (Analysis of symbolic sequences), 1999 – 2000
6. Project supported by the Natural Science Foundation of Yunnan Province: The research on thermodynamic formalism and universality of chaotic phenomena in nonlinear physical systems, Grant No. 97A007G, 1997 – 2000
Selected Publications
1. M. Xu, C.-Y. Xu, H. Wang, Y.-K. Li, J.-B. Hu and K.-F. Cao*, Global and partitioned reconstructions of undirected complex networks, Eur. Phys. J. B 89, 55 (2016).
2. H. Wang, J.-B. Hu, C.-Y. Xu, D.-H. Zhang, Q. Yan, M. Xu, K.-F. Cao* and X.-S. Zhang, A pathway-based network analysis of hypertension-related genes, Physica A 444, 928-939 (2016); 447, 569-570 (2016).
3. M. Xu, C.-Y. Xu, H. Wang, C.-Z. Deng and K.-F. Cao*, Analytical controllability of deterministic scale-free networks and Cayley trees, Eur. Phys. J. B 88, 168 (2015).
4. X.-S. Zhang* and K.-F. Cao, The impact of coinfections and their simultaneous transmission on antigenic diversity and epidemic cycling of infectious diseases, BioMed Res. Int. 2014, Article ID 375862, 23 pages (2014).
5. C.-Y. Xu, H. Wang, K.-F. Cao* and S.-L. Peng, A superconvergent universality induced by non-associativity, Phys. Lett. A 378, 1505-1509 (2014).
6. H. Wang, C.-Y. Xu, J.-B. Hu and K.-F. Cao*, A complex network analysis of hypertension-related genes, Physica A 394, 166-176 (2014).
7. W. Gao, C.-Y. Xu, S.-L. Peng, and K.-F. Cao*, Universal form of renormalizable knots in symbolic dynamics of bimodal maps, Int. J. Bifurcation and Chaos 23, 1350160 (2013).
8. Q. Liu, K.-F. Cao*, and S.-L. Peng, A generalized Kolmogorov-Sinai-like entropy under Markov shifts in symbolic dynamics, Physica A 388, 4333-4344 (2009).
9. Z. Zhou*, K.-F. Cao, and S.-L. Peng, New universal bifurcation scenario in one-dimensional trimodal maps, Phys. Lett. A 372, 3407-3414 (2008).
10. W.-B. Zhai, X.-Z. Chen, and K.-F. Cao*, Global multifractal relation between topological entropies and fractal dimensions, Chaos, Solitons & Fractals 23, 511-518 (2005).
11. K.-F. Cao, C. Zhang, and S.-L. Peng, Topological entropy, knots and star products, The Proceedings of the 14th European Conference on Iteration Theory (ECIT 2002, Évora, Portugal, 1-7 September 2002), edited by J. Sousa Ramos, D. Gronau, C. Mira, L. Reich, A. Sharkovsky, Grazer Math. Ber. 346, 61-72 (2004).
12. Y.-Y. Zhang and K.-F. Cao*, Metric universalities and systems of renormalization group equations for bimodal maps, Chaos, Solitons & Fractals 21, 457-471 (2004).
13. K.-F. Cao and S.-L. Peng*, Homology of vertex and edge shift matrices in symbolic dynamics and entropy invariants, Int. J. Mod. Phys. B 17, 4308-4315 (2003).
14. K.-F. Cao*, X.-S. Zhang, Z. Zhou, and S.-L. Peng, Devil’s carpet of topological entropy and complexity of global dynamical behavior, Chaos, Solitons & Fractals 16, 709-726 (2003).
15. Z. Zhou* and K.-F. Cao, An effective numerical method of the word-lifting technique in one-dimensional multimodal maps, Phys. Lett. A 310, 52-59 (2003).
16. K.-F. Cao*, Z. Zhou, W. Gao, and S.-L. Peng, General form of superuniversality for fractal dimensions in one-dimensional maps, Int. J. Mod. Phys. B 15, 4183-4197 (2001).
17. K.-F. Cao and S.-L. Peng, Complexity of routes to chaos and global regularity of fractal dimensions in bimodal maps, Phys. Rev. E 60, 2745-2760 (1999).
18. S.-L. Peng, X.-S. Zhang, and K.-F. Cao, Dual star products and metric universality in symbolic dynamics of three letters, Phys. Lett. A 246, 87-96 (1998).
19. S.-L. Peng and K.-F. Cao, Global scaling behaviors and chaotic measure characterized by the convergent rates of period-p-tupling bifurcations, Phys. Rev. E 54, 3211-3220 (1996).
20. J.-X. Shi, K.-F. Cao, T.-L. Guo and S.-L. Peng, Metric universality for the devil’s staircase of topological entropy, Phys. Lett. A 211, 25-28 (1996).
21. K.-F. Cao, Z.-X. Chen, and S.-L. Peng, Global metric regularity of the devil’s staircase of topological entropy, Phys. Rev. E 51, 1989-1995 (1995).
22. Z.-X. Chen, K.-F. Cao, and S.-L. Peng, Symbolic dynamics analysis of topological entropy and its multifractal structure, Phys. Rev. E 51, 1983-1988 (1995).
23. S.-L. Peng, K.-F. Cao, and Z.-X. Chen, Devil’s staircase of topological entropy and global metric regularity, Phys. Lett. A 193, 437-443 (1994); 196, 378 (1995).
24. K.-F. Cao and S.-L. Peng, Universal scaling of generalized dimensions on critical strange sets, J. Phys. A: Math. Gen. 25, 589-599 (1992).
25. K.-F. Cao, R.-L. Liu, and S.-L. Peng, A new universality for fractal dimensions of Feigenbaum-type attractors, Phys. Lett. A 136, 213-215 (1989).
26. S.-L. Peng and K.-F. Cao, A new global regularity of fractal dimensions on critical points of transitions to chaos, Phys. Lett. A 131, 261-264 (1988); 133, 543 (1988).
Supervision of Master's and Doctoral Students
Master's students (graduated: 31; training: 3)
Doctoral students (graduated: 4; training: 4)
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