基本情况

张祥，上海交通大学特聘教授（二级教授、博士生导师），享受国务院特殊津贴。2018年入选欧洲科学与艺术院院士。主要从事常微分方程的定性、分支和可积理论，以及奇异摄动理论及其应用等方面的研究。代表性研究成果发表在《American J. Mathematics》、《Advances in Mathematics》、《Communications in Mathematical Physics》、《Ergodic Theory and Dynamical Systems》、《J. Differential Equations》、《J. Functional Analysis》、《J. Nonlinear Sciences》、《Physical D》、《Pacific J. Mathematics》和《Transaction of American Mathematical Society》等国际重要数学期刊上。现已独立在Springer出版社出版专著《Integrable Theory of Dynamical Systems: Algebra and Analysis》和科学出版社出版教材《常微分方程》各一部。近年来多次应邀在德国、法国、西班牙、美国、加拿大、日本和墨西哥等召开的动力系统国际学术会议上做大会特邀报告。现任中国数学会奇异摄动专业委员会主任和上海市数学会理事（曾任中国数学会理事）。担任SCI杂志《Qualitative Theory of Dynamical Systems》和《International Journal of Bifurcation and Chaos》的Associate编辑。

 

研究领域

常微分方程与动力系统, 奇异摄动理论

 

教育背景

1994年9月至1997年6月 博士，南京大学，数学系

1988年9月至1991年6月 硕士，安徽师范大学，数学系

1984年9月至1988年6月 学士，安徽师范大学，数学系

 

工作经历

国内

2015年7月至今      特聘教授，上海交通大学

2002年8月至今     教授，博导（二级教授），上海交通大学

2001年10月至2002年7月 副教授，上海交通大学

2000年7月至2001年9月 副教授，南京师范大学

1997年7月至2000年6月 讲师，南京师范大学

1991年7月至1994年8月 助教，安徽师范大学

 

国外

2007年10月至2008年9月 访问教授，西班牙巴塞罗那数学研究中心 (合作研究)

2003年8月至2004年8月 访问教授，美国佐治亚理工学院(合作研究与教学)

1999年3月至2001年3月 博士后，西班牙巴塞罗那数学研究中心 (合作研究)

 

论文发表

专著和教材

  1. ZHANG Xiang, Integrability of dynamical systems: algebra and analysis. Developments in Mathematics, 47. Springer, Singapore, 2017.
  2. 张祥，常微分方程，科学出版社，2015 

代表性论文

  1. Qiao Qi and Zhang Xiang; Traveling waves to a chemotaxis-growth model with Allee effect. J. Differential Equations 416 (2025), 1747–1770.
  2. Yang Yantao, Zhang Xiang and Zu Jian;  Dynamics of a slow-fast Leslie-Gower predator-prey model with prey harvesting. Chaos 34 (2024), no. 10, Paper No. 103119, 19 pp.
  3. Chen Hebai, Yang Hao, Zhang Rui and Zhang Xiang; New criterions on nonexistence of periodic orbits of planar dynamical systems and their applications. J. Nonlinear Sci. 34 (2024), no. 5, Paper No. 96, 66 pp.
  4. Chen Hebai, Wang Lina and Zhang Xiang; A necessary and sufficient condition on algebraic limit cycles of a hybrid van der Pol–Rayleigh oscillator. J. Differential Equations 406 (2024),255–275.
  5. Qiao Qi and Zhang Xiang; The spectrum and stability of travelling pulses in a coupled FitzHugh-Nagumo equation. Sci. China Math. 67 (2024), no. 5, 975–1010.
  6. Xu Shoujun, Wu Hao and Zhang Xiang; On the local Gevrey integrability. J. Differential Equations 382 (2024), 246–273.
  7. Chen Hebai, Zhang Rui and Zhang Xiang; Dynamics of polynomial Rayleigh-Duffing system near infinity and its global phase portraits with a center. Adv. Math. 433 (2023), Paper No. 109326, 37 pp.
  8. Qiao Qi and Zhang Xiang; Traveling waves and their spectral stability in Keller-Segel system with large cell diffusion. J. Differential Equations 344 (2023), 807–845.
  9. Huang jianfeng, Liang Haihua and Zhang Xiang; A new Chebyshev criterion and its application to planar differential systems. J. Differential Equations 344 (2023), 658–695.
  10. Chen Hebai, Zhang Rui and Zhang Xiang; New criterions on stability and order of analytic nilpotent foci. J. Differential Equations 338 (2022), 352–371.
  11. Su Wei and Zhang Xiang; Global stability and canard explosions of the predator-prey model with the sigmoid functional response. SIAM J. Appl. Math. 82 (2022), no. 3,976–1000.
  12. Llibre Jaume and Zhang Xiang;  The Markus-Yamabe conjecture for continuous and discontinuous piecewise linear differential systems. Proc. Amer. Math. Soc. 149 (2021), no. 12, 5267–5274.
  13. Shen Jianhe and Zhang Xiang; Traveling pulses in a coupled FitzHugh-Nagumo equation. Phys. D 418 (2021), 132848.
  14. Yu Pei, Han Maoan and Zhang Xiang; Eighteen limit cycles around two symmetric foci in a cubic planar switching polynomial system. J. Differential Equations 275 (2021), 939–959.
  15. Walcher Sebastian and Zhang Xiang; Polynomial differential equations over the quaternions. J. Differential Equations 282 (2021), 566–595.
  16. Wei Lijun and Zhang Xiang, Limit cycles bifurcating from periodic orbits near a centre and a homoclinic loop with a nilpotent singularity of Hamiltonian systems. Nonlinearity 33 (2020), no. 6, 2723–2754.
  17. Villadelprat Jordi and Zhang Xiang; The period function of Hamiltonian systems with separable variables. J. Dynam. Differential Equations 32 (2020), no. 2, 741–767.
  18. Zhang Xiang; Homoclinic, heteroclinic and periodic orbits of singularly perturbed systems. Sci. China Math. 62 (2019), no. 9, 1687–1704.
  19. Wang Cheng and Zhang Xiang; Canards, heteroclinic and homoclinic orbits for a slow-fast predator-prey model of generalized Holling type III. J. Differential Equations 267 (2019), no. 6, 3397–3441.
  20. Llibre Jaume and Zhang Xiang; Limit cycles created by piecewise linear centers. Chaos 29 (2019), no. 5, 053116, 14 pp.
  21. Llibre Jaume and Zhang Xiang; The non-existence, existence and uniqueness of limit cycles for quadratic polynomial differential systems. Proc. Roy. Soc. Edinburgh Sect. A 149 (2019), no. 1, 1–14.
  22. Zhang Xiang, Dynamics of a nonlinear equation modelling the capillary rise. Phys. D 384/385 (2018), 34–38.
  23. Schlomiuk Dana and Zhang Xiang, Quadratic differential systems with complex conjugate invariant lines meeting at a finite point. J. Differential Equations 265 (2018), no. 8, 3650–3684.
  24. Wang Cheng and Zhang Xiang, Stability loss delay and smoothness of the return map in slow-fast systems. SIAM J. Appl. Dyn. Syst. 17 (2018), no. 1, 788–822.
  25. Wei Lijun and Zhang Xiang, Averaging theory of arbitrary order for piecewise smooth differential systems and its application. J. Dynam. Differential Equations 30 (2018), no. 1, 55–79.
  26. Han Maoan, Sheng Lijuan and Zhang Xiang, Bifurcation theory for finitely smooth planar autonomous differential systems. J. Differential Equations 264 (2018), no. 5, 3596–3618.
  27. Wei Lijun, Romanovski Valery and Zhang Xiang, Generalized involutive symmetry and its application in integrability of differential systems. Z. Angew. Math. Phys. 68 (2017), no. 6, Art. 132, 21 pp.
  28. Zhang Xiang, A note on local integrability of differential systems. J. Differential Equations 263 (2017), no. 11, 7309–7321.
  29. Zhang Xiang, Liouvillian integrability of polynomial differential systems, Transactions of the American Mathematical Society, 368 (2016), 607--620.
  30. Gine J, Llibre J, Wu Kesheng and Zhang Xiang, Averaging methods of arbitrary order, periodic solutions and integrability, J. Differential Equations 260 (2016), 4130--4156.
  31. Gasull Armengol, Torregrosa Joan, Zhang Xiang, The number of polynomial solutions of polynomial Riccati equations, Journal of Differential Equations，261 (2016), no 9, 5071--5093.
  32. Wei Lijun and Zhang Xiang, Normal form and limit cycle bifurcation of piecewise smooth differential systems with a center, Journal of Differential Equations 261 (2016), no. 2, 1399—1428
  33. Llibre Jaume and Zhang Xiang, Limit cycles of linear vector fields on manifolds, Nonlinearity, 29 (2016), no. 10, 3120--3131.
  34. Wei Lijun and Zhang Xiang, Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems, Discrete and Continuous Dynamical Systems 36 (2016), no. 5, 2803--2825.
  35. Weng Shiliang, Zhang Xiang, Integrability of vector fields versus inverse Jacobian multipliers and normaliers, Discrete and Continuous Dynamical Systems Series A 36 (2016), no. 11, 6539—6555