曹鸿钧

博士、教授

基本信息

办公电话：+86-010-51688453 电子邮件： hjcao@bjtu.edu.cn
通讯地址：北京市海淀区上园村3号，北京交通大学理学院数学系 邮编：100044

教育背景

1. 1981年9月至1985年7月，云南大学数学系数学专业；

2. 1985年7月至1995年7月，在云南楚雄师范专科学校（现云南楚雄师范学院）数学系工作；

3. 1995年9月至1998年7月，云南大学数学系数学专业硕士研究生，获理学硕士；

4. 1998年7月至2001年7月，中国科学院数学研究所博士研究生，动态系统分岔及混沌方向，获理学博士；

5. 2001年8月至2003年7月，在中国科学院软件研究所做博士后研究，从事并行计算及并行软件的研究；

6. 2003年8月起，在北京交通大学理学院数学系工作；

7. 2004年1月至4月，在香港城市大学电子工程系访问；

8. 2005年12月至2007年7月，在西班牙马德里国王大学数学与物理系做博士后，从事神经元科学的研究；

9. 2009年2月至3月, 在日本东京大学生产技术研究所Aihara实验室访问；
10. 2009年10月，北京交通大学，教授，博士生导师；
11. 2010年7月至9月,在香港城市大学电子工程系 Centre for Chaos and Complex Networks访问；
12. 2011年2月至3月, 在日本东京大学生产技术研究所Aihara实验室访问；

13. 2011年12月至2012年6月，美国马里兰大学数学系访问学者；

14. 2013年1月至2014年3月，香港理工大学电子及资讯工程学系访问学者；

15. 2016年3月至2016年4月，美国Johns Hopkins大学高级访问学者；

16. 2017年1月至2018年3月，美国得克萨斯大学阿灵顿分校高级访问学者；

17. 2018年12月至2019年6月，美国加州大学尔湾分校高级访问学者。

工作经历

研究方向

  • 应用数学

招生专业

  • 数学博士
  • 数学硕士

科研项目

  1. 智慧高铁系统前沿科学中心专项：高速列车转向架运行的稳定性与安全性研究， 2021-04-01-2023-03-31， 20万，主持。

  2. 国家自然科学基金“面上”：混杂离散神经元网络动态分析及应用，2012-01-01--2015-12-31，45.0万元，主持。

  3. 国家自然科学基金“面上”：基于映射的大尺度神经元网络聚合行为研究，2008-01-01--2010-12-31，28.0万元，主持。
  4. 北京市科委：混沌系统信息加密应用研究，2005-01-01--2007-12-31，10.0万元，主持。

教学工作

1. 本科生课程： 常微分方程；微分方程；非线性动态系统及应用；复变函数与积分变换；计算方法；数学研究方法.

2. 硕士生及博士生课程：微分方程基础；非线性动态系统的分岔与混沌；微分方程定性理论；分岔和混沌的数值计算及软件；神经元网络，常用数学软件及应用.

论文/期刊


49. Yue Li, Caihong Huang, Huailong Shi, Jing Zeng, Hongjun Cao. Dynamics of a high-speed railway wheelset with two time delays in primary suspension dampers. International Journal of Bifurcation and ChaosVol. 34, No. 08, 2024, 2450101. https://doi.org/10.1142/S0218127424501013.

 48. Xingang Wang, Hongjun Cao. Existence conditions for bifurcations of homoclinic orbits in a railway wheelset model. Communications in Nonlinear Science and Numerical Simulation. Volume 134, July, 2024, 107993.

 47. Yue Li, Caihong Huang, Jing Zeng, Hongjun Cao. Effect of motor suspension parameters on bifurcations for a nonlinear bogie system. DOI: 10.1080/00423114.2024.2305688, 2024, Vehicle System Dynamics.

 46. Penghe Ge, Libo Cheng, Hongjun Cao. Complete synchronization of three-layer Rulkov neuron network coupled by electrical and chemical synapses. Vol.34, Issue 4, 2024, https://doi.org/10.1063/5.0177771, DOI: 10.1063/5.0177771.

 45. Penghe Ge, Hongjun Cao. Dynamics of delayed neuroendocrine systems and their reconstructions using sparse identification and reservoir Computing. International Journal of Bifurcation and Chaos, Vol. 33, No. 6, 2023, 2330014 (23 pages).

44. Yue Li, Hongjun Cao. Bifurcation and comparison of a discrete-time Hindmarsh-Rose model. Journal of Applied Analysis and Computation. Volume 13, Number 1, February 2023, 34–56.

43. Huijing Sun, Hongjun Cao. The damping term makes the Smale-horseshoe heteroclinic chaotic motion easier. Discrete and continuous dynamical systems series B, 2022, 27, 8, 4685-4701. doi: 10.3934/dcdsb.2021247.

42. Peng Guo, Caihong Huang, Jing Zeng, Hongjun Cao. Hopf-Hopf bifurcation anaysis based on resonance and non-resonance in a simplified railway wheelset model. Nonlinear Dynamics. 2022, 108(2), 1197-1215. doi: 10.1007/s11071-022-07274-0.

 41. Yue Li, Caihong Huang, Jing Zeng, Hongjun Cao. Bifurcations in a simplified and smoothed model of the dynamics of a rolling wheelset. Nonlinear dynamics, 2022, 1-14. doi: 10.1007/s11071-022-07934-1.

40. Penghe Ge, Hongjun Cao. Intermittent evolution routes to the periodic or the chaotic orbits in Rulkov map. Chaos, Vol.31, Issue 9,September, 2021.https://doi.org/10.1063/5.0060205. DOI: 10.1063/5.0060205. 

39. Penghe Ge, Hongjun Cao.  Chaos in the Rulkov neuron model based on Marotto's theorem. International Journal of Bifurcation and Chaos. Vol. 31 No. 15, December, 2021.

38. Chunyan Zuo, Hongjun Cao. Extinction or coexistence of a predator-prey model with constant-yield harvesting. Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 27, 2020, 375-396.

37. Lifang Cheng, Hongjun Cao, Litao Zhang. Two-parameter bifurcation analysis of an aircraft nose landing gear model. Nonlinear Dynamics, 2021, 103:367–381.

https://doi.org/10.1007/s11071-020-06129-w. 

36. Penghe Ge, Xiukun Wei, Jinzhao Liu, Hongjun Cao. Bifurcation of a modified railway wheelset model with nonlinear equivalent conicity and wheel-rail force.Nonlinear Dynamics, 2020, 102(1),79-100.

35. Penghe Ge, Hongjun Cao. Synchronization of Rulkov neuron networks coupled by excitatory and inhibitory chemical synapses, Chaos, 29, 023129, 2019, https://doi.org/10.1063/1.5053908.

34. Lifang Cheng,Xiukun Wei,Hongjun Cao.Two-parameter bifurcation analysis of limit cycles of a simplified railway wheelset model, Nonlinear Dynamics, 93, 2415–2431, 2018.

33. Jingjing Li,Hongjun Cao.Different characteristics and important channels between the healthy brain network and the epileptic brain network based on EEG data, Communications in Nonlinear Science and Numerical Simulation, 66, 2019, 147–155, 2019.

32. Fengjuan Wang, Hongjun Cao. Mode locking and quasiperiodicity in a discrete-time Chialvo neuron model, Communications in Nonlinear Science and Numerical Simulation ,56,481-489,2018.

31. Lifang Cheng, Hongjun Cao. Effect of Higher Order Terms on the Bifurcation Structure of Coupled Rulkov Neurons,International Journal of Bifurcation and Chaos,11(27),17501781-175017819, 2017.

30. Lifang Cheng, Hongjun Cao. Synchronization Dynamics of Two Heterogeneous Chaotic Rulkov Neurons with Electrical Synapses,International Journal of Bifurcation and Chaos, 2(27),17300091-173000915, 2017.

29. Dongpo Hu, Hongjun Cao. Stability and bifurcation analysis in a predator-prey system with Michaelis-Menten type predator harvesting, Nonlinear Analysis: Real World Applications, 33:58-82, 2017.

28. Huijing Sun, Hongjun Cao. Complete synchronization of coupled Rulkov neuron networks, Nonlinear dynamics, 84(4), 2423-2434, 2016.

27. Huijing Sun, Hongjun Cao. Synchronization of two identical and non-identical Rulkov models, Communications in Nonlinear Science and Numerical Simulation, 40,15–27, 2016.

26. Lifang Cheng, Hongjun Cao. Bifurcation analysis of a discrete-time ratio-dependent predator–prey model with Allee Effect, Communications in Nonlinear Science and Numerical Simulation. 38 ,288–302, 2016.

25. Dongpo Hu, Hongjun Cao. Stability and Hopf bifurcation analysis in Hindmarsh-Rose neuron model with multiple time delays, International Journal of Bifurcation and Chaos,26(11),1650187, 2016.

24. Chunyan Zuo, Hongjun Cao. One of signatures of a memristor. Communications in Nonlinear Science and Numerical Simulation, Volume 30, Issues 1–3, Pages 128–138, January 2016.

23. Dongpo Hu, Hongjun Cao. Stability and synchronization of coupled Rulkov map-based neurons with chemical synapses. Communications in Nonlinear Science and Numerical Simulation, Volume 35, Pages 105-122, June 2016.

22. Caixia Wang,Hongjun Cao. Stability and chaos of Rulkov map-based neuron network with electrical synapse. Communications in Nonlinear Science and Numerical Simulation, 20：536-545, 2015.

21. Yang Yu, Hongjun Cao. Intergral step size makes a difference to bifurcations. Int. J. Bifurcation and Chaos. 25(2)：1550029-1550046, 2015.

20. Dongpo Hu, Hongjun Cao. Bifurcation and chaos in a discrete-time predator-prey system of Holling and Leslie type. Communications in Nonlinear Science and Numerical Simulation. 22,1-3, 702-715, 2015.

19. Caixia Wang, Hongjun Cao. Parameter space of the Rulkov chaotic neuron model, Communications in Nonlinear Science and Numerical Simulation.19, 2060–2070, 2014.

18. Hongjun Cao, Yanguo Wu. Bursting types and stable domains of Rulkov neuron network with mean field coupling. International Journal of Bifurcation and Chaos, Vol. 23, No. 12, 2013, 1330041-1330061.

17. Meixiang Cai, Hongjun Cao. Bifurcations of periodic orbits in Duffing equation with periodic damping and external excitations. Nonlinear Dynamics,  2012, Volume 70. Issue 1, 453-462.

16. Hongjun Cao and Borja Ibarz. Hybrid Discrete-Time Neural Networks. Phil. Trans. R. Soc. A 368, 2010, 5071–5086.

15. Borja Ibarz, Hongjun Cao, and Miguel A. F. Sanjuán. Bursting regimes in map-based neuron models coupled through fast threshold modulation, Physical Review E. 2008, 77, 051918.

14. Hongjun Cao, Caixia Wang, Miguel A. F. Sanjuán.Effect of the Step Size on Bifurcations and Chaos of a Map-based BVP Oscillator. Int. J. Bifurcation and Chaos，2010, 12, 20（6）.

13. Hongjun Cao, Miguel A.F.Sanjuan.A mechanism for elliptic-like bursting and synchronization of bursts in a map-based neuron network. Cognitive Processing, 2009, 12, Vol.1（No. 10）.

12. Hongjun Cao, Jesus M. Seoane,Miguel A.F. Sanjuan.Symmetry-breaking analysis for the general Helmholtz-Duffing oscillator. Chaos, Solitons and Fractals, 2007, 12，34.

11. Huijing Sun, Hongjun Cao, Chaos control and synchronization of a modified chaotic system, Chaos, Solitons & Fractals, Vol. 37, Issue 5, September 2008, 1442-1455.

10. Huijing Sun, Hongjun Cao, Bifurcations and chaos of a delayed ecological model, Chaos, Solitons & Fractals, Vol. 33, Issue 4, August 2007, 1383-1393.

9. Hongjun Cao, Yaozheng Jiang, and Yulin Shan, Primary resonant optimal control for nested homoclinic and heteroclinic bifurcations in single-dof nonlinear oscillators, Journal of Sound and Vibration, Vol. 289, Issues 1-2, 3 January 2006, 229-244.

8. Peipei Zhou, Hongjun Cao, The effect of symmetry-breaking on the parameterically excited pendulum, Chaos, Solitons & Fractals, Volume 38, Issue 2, October, 2008, 590-597.

7. Hongjun Cao. Primary resonant optimal control for homoclinic bifurcations in singie-degree-of-freedom nonlinear oscillators. CHAOS SOLITONS &FRACTALS，2005, 12, 24.

6. Hongjun Cao, Guanrong Chen. Global and local contral of homoclinic and heteroclinic bifurcations[J]. International Journal of Bifurcation and Chaos，2005, 12, 15（8）.

5. Hongjun Cao, Guanrong Chen,Xuebin Chi.Suppressing or inducing chaos in amodel of robot arms and mechanical manipulators. Journal of Sound and Vibration, 2004, 12.

4. Hongjun Cao, Guanrong Chen,Xuebin Chi.Suppressing or inducing chaos by Weak Resonant Excitations in an Externally-Forced Froude Pendulum. International Journal of Bofurcation and Chaos, 2004, 12, 14（3）.

3. Hongjun Cao, Zhengrong Liu, and Zhujun Jing, Bifurcations set and distribution of limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms, Chaos, Solitons and Fractals, Vol. 14, 2000, 2293-2304.

2. Zhujun Jing, and Hongjun Cao, Bifurcations of periodicorbits in Josephson equation with phase shifts, Int. J.Bifurcation and Chaos, Vol. 12, No. 7, 2002, 1515-1530.

1. Hongjun Cao, and Zhujun Jing, Chaotic dynamics of Josephson equation driven by ac and dc current forcings, Chaos, Solitons and Fractals, Vol. 12, No. 10, 2001, 1887-1895. 




专著/译著

专利

软件著作权

获奖与荣誉

社会兼职

美国数学会Mathematical Review评论人，多家国内外专业杂志审稿人。