The goal of this project is to obtain the properties of invariant sets in some dynamical models and investigate the influence of small perturbations for the systems. We concentrate on the mathematical problems of versal unfoldings and bifurcations of planar polynomial differential systems with high degree. Specially, we classify some systems of high degree, which have centers or degenerate equilibria. Then we study the degeneracy and unfolding of the systems. The bifurcations of unfolding systems near degenerate equilibria or centers are further investigated. Finally, the topological phase portraits of the systems are present and rigorous mathematical explanation of our results in the models for applications is given.
We investigated the problems of isochronicity, linearizability and critical period bifurcation of planar differential systems, limit cycles of discontinuous piecewise perturbations of a linear center, global dynamics and unfoldings of planar smooth and piecewise smooth quasi-homogeneous differential systems, unfoldings of odd Lienard systems, and global dynamics of epidemic models and autocatalator models respectively.
In this project, we not only solve some classical and difficult mathematical problems in the field of dynamical systems, but also our research on general differential systems can be applied in some mathematical models of real word phenomena.
 W. Fernandes, V. G. Romanovski, M. Sultanova, Y. Tang*, Isochronicity and linearizability
of a planar cubic system, J. Math. Anal. Appl.,
450 (2017) 795–813. [PDF]
 Y. Tang, D. Xiao*, W. Zhang, D. Zhu,
Dynamics of epidemic models with asymptomatic infection and seasonal succession,
Mathematical Biosciences and Engineering, 14(2017) 1407
– 1424. [PDF]
. V. G. Romanovski, W.Fernandes, Y. Tang*, Y. Tian, Linearizability and
critical period bifurcations of a generalized Riccati system, Nonlinear Dynamics,
https://doi.org/10.1007/s11071-017-3659-y or available as 'Online
 Y. Tang*, W. Zhang, Versal unfolding of a nilpotent Lienard equilibrium within the Lienard family, preprint. [PDF]
 V. G. Romanovski, Y. Tang*, Stevan Macesic, Global dynamics of an autocatalator model, preprint. [PDF]