1.向量场的分支理论
2.切换系统的分支理论
3.希尔伯特第16问题， 弱化希尔伯特第16问题
4.生物数学中微分方程模型及定性分析
1．主持国家自然科学基金面上项目：（项目批准号：11671040，2017.1---2020.12， 分段光滑系统的分支理论）
2．参加北京师范大学自主科研项目：无穷维动力系统中的一些问题及其应用（2016.1-2018.12）
[1] 赵丽琴, 一类五次向量场在非对称扰动下 Abel 积分零点的个数, 中国科学: 数学, 2017年第47卷第1期: 227-240.
[2] Jihua Yang, Liqin Zhao, Limit cycle bifurcations for piecewise smooth integrable differential systems, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES B, doi:10.3934/dcdsb.2017123.
[3] Jihua Yang, Liqin Zhao, Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop, International Journal of Bifurcation and Chaos, Vol. 26, No. 12 (2016) 1650204 (14 pages)
[4]Xianbo Sun, Liqin Zhao, Perturbations of a class of hyper-elliptic Hamiltonian systems of degree seven with nilpotent singular points, Applied Mathematics and Computation, 289(2016) 194-203.
[5] L.Zhao, Bifurcations of limit cycles in equivariant quintic planar vector fields,J. Math.Anal. Appl.422(2015)352-375.
[6]L.Zhao，The perturbations of a class of hyper-elliptic Hamilton systems with a double homoclinic loop through a nilpotent saddle, Nonlinear Anal.95 (2014)374-387.
[7]L.Zhao, D.Li, Bifurcations of limit cycles from a quintic Hamiltonian system with a heteroclinic cycle,Acta Math.Sin.(Engl.Ser.)30 (2014)411-422.
[8] L.Zhao, M.Qi, C.Liu, The cyclicity of period annuli of a class of quintic Hamiltonian systems, J. Math.Anal.Appl.403(2013)391-407.
[9]M.Qi, L.Zhao, Bifurcations of limit cycles from a quintic Hamiltonian system with a figure double-fish, Internat.J. Bifur. Chaos Appl. Sci.Engrg. 23(2013)1350116,15 pp.
[10]L.Zhao, Z.Fan, The number of small amplitude limit cycles in arbitrary polynomial systems, J. Math.Anal.Appl.407(2013)237-249.
毕业博士：2名； 在读博士：1名；2017.9入学硕士：2名
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