UBPDS · Unfoldings and Bifurcations of Polynomial Differential Systems

Unfoldings and Bifurcations of Polynomial Differential Systems

The main objective of this project is to obtain the properties of invariant sets in some dynamical models, to investigate the influence of small perturbations for the systems, and to analyze dynamics of real world models in biology and chemistry. For these purposes, 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. For example, the theoretical results in our investigation of practical models provide an intuitive basis for understanding the evolution of the epidemic and the nonlinear chemical reaction steps of the prototype autocatalator, which allow us to predict the outcomes of control strategies during the course of the epidemic and the autocatalator.

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