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云南大学物理与天文学院研究生导师介绍：曹克非
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. 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-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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