Education 

July,1998, Ph.D.in Pure Mathematics, University of Science and Technology of China. Hefei, China.

Thesis Title: Studies on some topics in topology and geometry and the applications.

Employment

July 1998-Apr,2002, Professor of Applied Mathematics, Chongqing University of Post and Tech. Chongqing, China

Apr,2002,--Mar,2004, Professor of Control and Systems theory, Xiamen University Xiamen, China

Mar. 2004,---present, Professor of Mathematics, Huazhong University of Sci. and Tech. Wuhan, China

Research interests

General interests:  

Dynamical systems, differential topology, geometric control and animal

locomotion, the secrets of the sound of violin.

Current interests:  

Dynamical systems theory and applications, injectivity of local diffeomorphic maps,

geometric control and mathematical modeling of the vibration of violin

Teaching  

Undergraduate course “ Mathematical control theory”

Graduate course “ topology”

Hobbies

Music：Classical music, playing the violin and the Bayan (button) accordion

Games: Pingpong ball, badminton.

PUBLICATIONS (-2019)

More than 100 journal papers, 3 books, with an h-index=26 (ISI)

Selected publications

Dynamical systems and chaos

1 Xiao-Song Yang, Index sums of isolated singular points of positive vector fields, Discrete and Continuous Dynamical System –A, 25(3), 1033–1039, 2009.

2 Songmei Huan and Xiao-Song Yang，On the number of limit cycle in general planar piecewise linear systems，Discrete and Continuous Dynamical System –A，Volume 32, Number 6, June 2012 pp. 2147-2164。

3 Xiao-Song Yang, Estimate of topological entropy of N-buffer switched networks, Nonlinearity，18(2005) 263-275.

4 Xiao-Song Yang* and Suochun Zhang, On possibility of creating new asymptotically stable periodic orbits in continuous time dynamical systems by small feedback control, Nonlinearity,16(2003), 1853-1959.

5 Xiao-Song Yang, Topological horseshoes and computer assisted verification of chaotic dynamics，t. J. Bifurcation and Chaos，19 (2009) 1127–1145

7 Qingdu Li, Xiao-Song Yang , Chaotic dynamics in a class of 3D Glass networks, Chaos 16(3),033101 （2006）5 pages,

8 Xiao-Song Yang, Yan Huang， Complex dynamics in simple Hopfield neural networks Chaos16(2006) Article Number: 033114 DOI: 10.1063/1.2220476

9 Songmei Huan and Xiao-Song Yang*，Generalized Hopf bifurcation in a class of planar switched systems，Dynamical Systems Vol. 26, No. 4, December 2011, 433–445

10 Xiao-Song Yang et al, A planar topological horseshoe theory with applications to computer verifications of chaos, J. Phys. A: Math. Gen. 38 (2005) 4175–4185

11 Qingdu Li, Xiao-Song Yang , A computer-assisted verification of hyperchaos in the Saito hysteresis chaos generator, J. Phys. A: Math. Gen. 39 (2006) 9139-9150.

12 Xiao-Song Yang, On existence of subharmonic orbits in Hamiltonian systems, Bulletin of Polish Academy of Science Vol. 48, No.2 (2000), 221-225.

13 Song-Mei Huan, Xiao-Song Yang∗，Existence of limit cycles in general planar piecewise linear systems of saddle–saddle dynamics，Nonlinear Analysis 92 (2013) 82–96

14 Lei Wang and Xiao-Song Yang， A vast amount of various invariant tori in the Nosé-Hoover oscillator， Chaos， 25, 123110 (2015); doi: 10.1063/1.4937167

15 Tiantian Wu, Lei Wang & Xiao-Song Yang，Chaos generator design with piecewise affine systems，Nonlinear Dynamics, 84(2016), 817-832

16 Tiantian Wu and Xiao-Song Yang_ A NEW CLASS OF 3-DIMENSIONAL PIECEWISE AFFINE SYSTEMS WITH HOMOCLINIC ORBITS， Discrete and Continuous Dynamical System –A，Vol. 36, Number 9, September 2016 pp. 5119-5129

17 Tiantian Wu and Xiao-Song Yang，On the existence of bifocal heteroclinic cycles in a class of four-dimensional piecewise affine systems，Chaos 26, 053104 (2016); doi: 10.1063/1.4949474

18 Song-Mei Huan∗ and Xiao-Song Yang，On the Number of Invariant Cones and Existence of Periodic Orbits in 3-dim Discontinuous Piecewise Linear Systems，International Journal of Bifurcation and Chaos, Vol. 26, No. 3 (2016) 1650043 (12 pages)

19 Xiao-Song Yang，Tiantian Wu， A Note on Phase Coherence of Chaotic Sets，International Journal of Bifurcation and Chaos, Vol. 26, No. 14 (2016) 1650243 (14 pages)

20 Lei Wang ，Xiao-Song Yang，Heteroclinic cycles in a class of 3-dimensional piecewise affine systems, Nonlinear Analysis: Hybrid Systems 23 (2017) 44–60

21 Tiantian Wu ，Xiao-Song Yang，On the existence of homoclinic orbits in n-dimensional piecewise affine systems，Nonlinear Analysis: Hybrid Systems 27 (2018) 366–389

22 Lei Wang ，Xiao-Song Yang ，The existence and stability analyses of periodic orbits in 3-dimensional piecewise affine systems，Nonlinear Analysis: Hybrid Systems 27 (2018) 157–173

23 Tiantian Wu1, and Xiao-Song Yang，Horseshoes in 4-dimensional piecewise affine systems with bifocal heteroclinic cycles, CHAOS 28, 000000 (2018)

24 Lei Wang ·Xiao-Song Yang, Singular cycles connecting saddle periodic orbit and saddle equilibrium in piecewise smooth systems, Nonlinear Dyn, doi.org/10.1007/s 11071-019-05142-y

25 Xiao-Song Yang and Lei Wang, Period-Increasing Indicates Loss of Stability, International Journal of Bifurcation and Chaos, Vol. 29, No. 12 (2019) 1950159 Mathematical biology Lei Wang，Xiao-Song Yang，Topological horseshoe and its uniform hyperbolicity in the HP model，J. Math. Biol.，DOI 10.1007/s00285-016-1076-3

Dynamics in Robotics

1 Qingdu Li, and Xiao-Song Yang*，New walking dynamics in the simplest passive bipedal walking model , Applied Mathematical Modelling， 36 (2012) 5262–5271

2 Qingdu Li, Song Tang, and Xiao-song Yang∗，New bifurcations in the simplest passive walking model，Chaos 23, 043110 (2013); doi: 10.1063/1.4824975

3 Qingdu Li, Jianli Guo, and Xiao-Song Yang , Bifurcation and chaos in the simple passive dynamic walking model with upper body, Chaos: 24, 033114 (2014); doi: 10.1063/1.4890834

Control theory

1 Xiao-Song Yang, Remarks on three types of asymptotic stability, Systems and Control Letters, 42 (2001), 299-302

2 Shidong Zhai, and Xiao-Song Yang, Stability analysis of feedback switched systems with state and switching delays, IMA Journal of Mathematical Control and Information (2012),doi:10.1093/imamci/dns010

3 Shidong Zhai, Xiao-Song Yang, Dwell time approach to L2-induced gain analysis of

discrete-time switched systems subject to actuator saturation, IET_CTA-2012-0508。

4 Zhai Shidong,Yang Xiao-Song*，Contraction analysis of synchronization of complex switched networks with different innercoupling matrices，Journal of the Franklin Institute, 350(2013),3116–3127

Design of chaotic circuits

1 X.S. Yang and Q. Li, Chaos generator via Wien-bridge oscillator, Electronic Letters Vol. 38,2002, pp.623-625.

2 Qingdu Li, Xiao-Song Yang*, A new multiple-scrolls chaotic attractor and its circuit implementation, Electronic Letters， 39(2003), 1306-1307.

Differential geometry：

S S Yang (X.-S Yang), Isometric immersion of compact Riemannian manifold into En+m with mean curvature pinched, Publ. Math. Debrecen 52/1-2 (1998), 79-83.

Topology and relevant topics：

1 Xiao-Song Yang, Topology of singular fiber bundles, Expo. Math 17(1999), 275-282.

2 Xiao-Song Yang, On topological classification of singular fiber bundles with 2-D base space,

Expos. Math., 17(1999), 359-364

3 Xiao-Song Yang, On coincidences of continuous maps, Nonlinear Analysis, 50(2002)

913-918.

4 Xiao-Song Yang，An Index Theory for Positive Dynamical Systems with an Application to Lotka–Voterra Systems，Qual. Theory Dyn. Syst. 12(2013),305–314

5 Xiao-Song Yang, Index sums of isolated singular points of positive vector fields, Discrete and Continuous Dynamical System –A, 25(3), 1033–1039, 2009.

6 Xiao-Song Yang, Construction of smooth sphere maps with given degrees and a generalization of Morse index formula, Qual. Theory Dyn. Syst. (2015) 14:139–147

Books

Xiaosong Yang， Topological theory of Hamiltonian systems, USTC Press， Hefei， 2000，（in Chinese）Xiaosong Yang and Qingdu Li, Chaotic systems and chaotic circuits, Science Press, Beijing, 2007 ( in Chinese)

Xiaosong Yang, An introduction to mathematical control theory, Science Press Beijing, 2012 ( in Chinese)