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曹克非，男，1963年11月生于云南省昆明市，教授（二級(jí)崗），博士生導(dǎo)師，云南省中青年學(xué)術(shù)和技術(shù)帶頭人。任《云南大學(xué)學(xué)報(bào)（自然科學(xué)版）》編委�，F(xiàn)在云南大學(xué)物理與天文學(xué)院物理系、非線性復(fù)雜系統(tǒng)中心工作，主要從事復(fù)雜網(wǎng)絡(luò)、非線性復(fù)雜系統(tǒng)、混沌、普適性、符號(hào)動(dòng)力學(xué)和分形等方面的研究。曾作為青年成員承擔(dān)完成國(guó)家“九五”攀登計(jì)劃非線性科學(xué)項(xiàng)目子課題，承擔(dān)完成“十五”國(guó)家重點(diǎn)基礎(chǔ)研究發(fā)展規(guī)劃（“973”計(jì)劃）非線性科學(xué)項(xiàng)目子課題；主持完成國(guó)家自然科學(xué)基金項(xiàng)目、教育部高等學(xué)校博士學(xué)科點(diǎn)專項(xiàng)科研基金項(xiàng)目、云南省自然科學(xué)基金項(xiàng)目；并作為主要成員參加過(guò)多項(xiàng)國(guó)家自然科學(xué)基金項(xiàng)目、云南省級(jí)重點(diǎn)和面上項(xiàng)目以及云南省政府省院省校合作項(xiàng)目。在美國(guó)、英國(guó)、荷蘭、法國(guó)、德國(guó)、新加坡等出版的國(guó)際物理學(xué)期刊上發(fā)表了多篇論文。

研究工作經(jīng)歷

1997/05 – ，云南大學(xué)物理系、非線性復(fù)雜系統(tǒng)中心，教授

1983/09 – 1997/05，云南民族學(xué)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(guó)利茲大學(xué)生理系、非線性研究中心，訪問(wèn)學(xué)者

獲獎(jiǎng)情況

1. 2000年度云南省科學(xué)技術(shù)獎(jiǎng)自然科學(xué)類一等獎(jiǎng)（一維多符號(hào)動(dòng)力學(xué)中的星花積，排名第二，2001/09）

2. 云南省有突出貢獻(xiàn)的優(yōu)秀專業(yè)技術(shù)人才二等獎(jiǎng)（2000/10）

3. 首屆云南省自然科學(xué)獎(jiǎng)一等獎(jiǎng)（非線性符號(hào)動(dòng)力學(xué)與超費(fèi)根鮑姆普適性，排名第二，1996/05）

4. 國(guó)務(wù)院政府特殊津貼（1993/10 – ）

承擔(dān)的主要科研項(xiàng)目（主持）

1. 國(guó)家自然科學(xué)基金項(xiàng)目（分形網(wǎng)絡(luò)系統(tǒng)的幾何動(dòng)力學(xué)分析，11365023，2014 – 2017，在研）

2. 國(guó)家自然科學(xué)基金項(xiàng)目（符號(hào)動(dòng)力學(xué)中的非規(guī)范星花積與新型超收斂普適性，10565004，2006 – 2008，已結(jié)題）

3. 教育部高等學(xué)校博士學(xué)科點(diǎn)專項(xiàng)科研基金項(xiàng)目（非線性復(fù)雜系統(tǒng)中的特征量及相互關(guān)系分析，20050673001，2006 – 2008，已結(jié)題）

4. 國(guó)家重點(diǎn)基礎(chǔ)研究發(fā)展規(guī)劃（“973”計(jì)劃）“非線性科學(xué)中的若干前沿問(wèn)題”項(xiàng)目子課題（符號(hào)序列的復(fù)雜性分析：符號(hào)序列的復(fù)雜性與新度量普適性分析，任復(fù)雜性課題組副組長(zhǎng)，G2000077308，2000 – 2005，已結(jié)題）

5. 國(guó)家“九五”攀登計(jì)劃“非線性科學(xué)”項(xiàng)目子課題（符號(hào)序列分析，青年成員，1999 – 2000，已結(jié)題）

6. 云南省自然科學(xué)基金項(xiàng)目（非線性物理系統(tǒng)混沌現(xiàn)象的熱力學(xué)形式與普適性研究，97A007G，1997 – 2000，已結(jié)題）

發(fā)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(dǎo)研究生情況

碩士研究生（畢業(yè)31人，在讀3人）

博士研究生（畢業(yè)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)