Liu, Xingbo ( 刘兴波 )
| Title： | Professor |
|---|---|
| Department： | Applied Mathematics |
| Office： | Room 215, Stat Building |
| Telephone： | 54342646-615 |
| Email： | xbliu@math.ecnu.edu.cn |
| Homepage： | http://math.ecnu.edu.cn/~xbliu |
| Homepage2： | https://faculty.ecnu.edu.cn/_s42/lxb/main.psp |
Research Interest
Bifurcation theory and chaos of dynamical system
Resume
Resume:
1992．9―1992。7 烟台师范学院数学系本科。
1996．9―1999。7 山东矿业学院数学系硕士研究生。
1999．9---2002。7 华东师范大学数学系博士
2002-至今 华东师范大学数学系
主讲课程：
常微分方程，本科必修，
常微分方程定性理论，研究生专业课，
常微分方程续论，研究生基础课，
高等数学B， 公共课，
高等数学C， 公共课，
Selected Publications
Papers:
[1] 刘兴波，韩茂安. 一类两点异宿环的扰动分支，数学年刊，21：6（2000）
[2] 金银来、李先义、刘兴波 .非扭曲退化同宿分支,数学年刊, 22: 4 (2001)
[3] Liu X. B., Zhu D.M., Some topological properties of endomorphisms of the unit circle. Ann. of. Diff .Eqs. 19(3) 2003.
[4] Han. M .A, Hu .S. C., Liu .X. B., On stability of double homoclinic and heteroclinic cycles, Nonlinear analysis, 53, 2003.
[5] 刘兴波, 朱德明. 同宿流形中的奇异轨道, 高校应用数学学报, 18 (2) 2003.
[6] 刘兴波, 朱德明. 奇摄动下的共振不变环面分支,
数学年刊, 5, 2004.
[7] 刘兴波, 朱德明. 伴随超临界分支的通有同宿轨道分支.
数学学报, 5, 2004.
[8] 刘兴波, 朱德明. 快变振荡下的同宿轨道分支 ，数学物理学报，2005 （6）
[9]、Liu
X.B., Fu X.L., Zhu D.M., Bifurcation of homoclinic orbits with saddle-center
equilibrium., Chin.Ann.Math (B) 2006.
[10]、Liu X .B., Fu X.L., Zhu D.M.,homoclinic bifurcation with nonhyperbolic equilibria, Nonlinear analysis, ( accepted).
Recent Publications(From MathSciNet)
MR5047458
Prelim
Zhu, Zirui; Liu, Xingbo; Multiple limit cycles in a piecewise-smooth predator-prey model with additive Allee effect.
Bull. Sci. Math. 211 (2026), Paper No. 103818, 34 pp. 34C07 (34A36 34C23)
Publication Year 2026
MR5039494
Pending
Li, Zhengkang; Liu, Xingbo; Tian, Yuanyuan Existence of homoclinic orbits in three-dimensional piecewise linear forced oscillator systems.
Bull. Sci. Math. 209 (2026), Paper No. 103804, 33 pp. 34C37 (34A36 34C23 37G20)
Publication Year 2026
Indexed 2026-05-04
MR5011153
Reviewed
Li, Zhengkang; Liu, Xingbo Existence and stability of slow-fast traveling pulses in a chemical system with quintic nonlinearity.
J. Dynam. Differential Equations 38 (2026), no. 1, 143–181. 34E15 (34C37 35C07 92E99)
Publication Year 2026
Indexed 2026-05-13
Review Published2026-05-27
MR4964463
Reviewed
Fu, Yanxue; Liu, Xingbo Dynamics of a spatio-temporal slow-fast predator-prey system with reproductive Allee effect and a generalist predator.
Qual. Theory Dyn. Syst. 24 (2025), no. 5, Paper No. 223, 49 pp. 34E15 (34D15 35C07 35K57 92D25)
Publication Year 2025
Indexed 2025-11-19
Review Published2025-11-25
MR4954590
Pending
Hua, Duo; Liu, Xingbo Limit cycle bifurcations near nonsmooth homoclinic cycle in discontinuous systems.
J. Dynam. Differential Equations 37 (2025), no. 3, 2513–2538. 37G20
Publication Year 2025
Indexed 2025-10-23
MR4851141
Reviewed
Dong, Huimiao; Liu, Xingbo Traveling front in a diffusive predator-prey model with Beddington-DeAngelis functional response.
Math. Methods Appl. Sci. 48 (2025), no. 3, 3682–3711. 35C07 (35K57)
Publication Year 2025
Indexed 2025-03-24
Review Published2025-03-26
MR4839488
Reviewed
Hua, Duo; Liu, Xingbo Dynamics near the three-point heteroclinic cycles with saddle-focus.
Bull. Sci. Math. 199 (2025), Paper No. 103562, 35 pp. (Reviewer: Zhouchao Wei) 34C37 (34C23 37G15)
Publication Year 2025
Indexed 2025-02-21
Review Published2025-06-16
MR4753249
Reviewed
Hua, Duo; Liu, Xingbo Bifurcations of degenerate homoclinic solutions in discontinuous systems under non-autonomous perturbations.
Chaos 34 (2024), no. 6, Paper No. 063109, 13 pp. 34C23 (34A36 37G20)
Publication Year 2024
Indexed 2024-07-31
Review Published2024-08-14
MR4726196
Reviewed
Zhu, Zirui; Xu, Yancong; Liu, Xingbo; Ruan, Shigui Modeling the p53-Mdm2 dynamics triggered by DNA damage.
J. Nonlinear Sci. 34 (2024), no. 3, Paper No. 47, 50 pp. (Reviewer: Jinzhi Lei) 34C23 (34C25 34C37 92D25)
Publication Year 2024
Indexed 2024-06-06
Review Published2025-07-15
MR4671517
Reviewed
Zhu, Zirui; Liu, Xingbo Existence of traveling wave solutions in a singularly perturbed predator-prey equation with spatial diffusion.
Discrete Contin. Dyn. Syst. 44 (2024), no. 1, 78–115. 35C07 (35K40 35K55 92D25)
Publication Year 2024
Indexed 2024-01-25
Review Published2024-02-20
MR4655460
Reviewed
Hua, Duo; Liu, Xingbo Computer-assisted analysis of chaos in a three-species food chain model.
Stud. Appl. Math. 151 (2023), no. 3, 1166–1191. 92D25 (34C28 92D40)
Publication Year 2023
Indexed 2023-11-20
Review Published2024-01-16
MR4652598
Reviewed
Li, Zhengkang; Liu, Xingbo Singular perturbation analysis in a coupled Chua's circuit with diffusion.
Chaos 33 (2023), no. 10, Paper No. 103118, 18 pp. (Reviewer: Maximilian Engel) 34E15 (34D35 35C07 37C29 37M05)
Publication Year 2023
Indexed 2023-12-13
Review Published2025-03-14
MR4650070
Reviewed
Zhu, Zirui; Liu, Xingbo Singular perturbation analysis for a Holling-Tanner model with additive Allee effect.
Internat. J. Bifur. Chaos Appl. Sci. Engrg. 33 (2023), no. 12, Paper No. 2350142, 25 pp. 92D25 (37N25)
Publication Year 2023
Indexed 2023-12-01
Review Published2024-01-03
MR4557479
Reviewed
Hua, Duo; Liu, Xingbo Dynamical analysis in a piecewise smooth predator-prey model with predator harvesting.
Int. J. Biomath. 16 (2023), no. 6, Paper No. 2250118, 22 pp. (Reviewer: Hongying Shu) 92D25 (34A36 34C23 34C37 37N25)
Publication Year 2023
Indexed 2023-05-02
Review Published2023-07-17
MR4527356
Reviewed
Li, Zhengkang; Liu, Xingbo Impact limit cycles in the planar piecewise linear hybrid systems.
Commun. Nonlinear Sci. Numer. Simul. 119 (2023), Paper No. 107074, 16 pp. (Reviewer: Pei Yu) 34A36 (34C07)
Publication Year 2023
Indexed 2023-02-27
Review Published2023-07-28
MR4512850
Reviewed
Dong, Huimiao; Zhang, Tiansi; Liu, Xingbo Bifurcations of double heterodimensional cycles with three saddle points.
J. Appl. Anal. Comput. 12 (2022), no. 6, 2143–2162. 34C23 (34C29 34C37)
Publication Year 2022
Indexed 2023-02-06
Review Published2023-08-29
MR4474081
Reviewed
Li, Zhengkang; Liu, Xingbo Limit cycles in discontinuous piecewise linear planar Hamiltonian systems without equilibrium points.
Internat. J. Bifur. Chaos Appl. Sci. Engrg. 32 (2022), no. 10, Paper No. 2250153, 20 pp. 34C07 (37J25)
Publication Year 2022
Indexed 2022-10-25
Review Published2022-11-22
MR4457695
Reviewed
Li, Zhengkang; Liu, Xingbo Homoclinic orbits in three-dimensional continuous piecewise linear generalized Michelson systems.
Chaos 32 (2022), no. 7, Paper No. 073128, 18 pp. 37C29 (34C37 35C07)
Publication Year 2022
Indexed 2022-10-03
Review Published2022-10-25
MR4412459
Reviewed
Zhu, Zirui; Liu, Xingbo Canard cycles and relaxation oscillations in a singularly perturbed Leslie-Gower predator-prey model with Allee effect.
Internat. J. Bifur. Chaos Appl. Sci. Engrg. 32 (2022), no. 5, Paper No. 2250071, 23 pp. 92D25 (37C29)
Publication Year 2022
Indexed 2022-06-21
Review Published2022-07-06
MR4311461
Reviewed
Li, Zhengkang; Liu, Xingbo Limit cycles in the discontinuous planar piecewise linear systems with three zones.
Qual. Theory Dyn. Syst. 20 (2021), no. 3, Paper No. 79, 22 pp. 34C07 (34A36)
Publication Year 2021
Indexed 2021-10-26
Review Published2022-07-07
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