In this paper, a p53-Mdm2 network model with Michaelis–Menten function involved in DNA damage repair is studied by using the dynamical system approach. Detailed bifurcations of the model including saddle-node bifurcation, Hopf bifurcation of codimension 3, and cusp-type Bogdanov–Takens bifurcation of codimension 3 are investigated. To our best knowledge, it is the first time that the coexistence of an isola and a cusp of limit cycles is observed for the p53 model, which indicates complex transitions of different oscillating dynamics. Furthermore, we find that oscillation could persist whether the damage is nonexistent, small or large, and multiple oscillations can be involved in the DNA repair process. In addition, the dynamics induced by the interaction between p53 and Mdm2 unveil the relationship between the positive feedback brought by p53 itself and the negative feedback brought by Mdm2, which triggers the digital oscillation modes for DNA damage. Of particular interest is that multiple oscillations and the threshold value of DNA damage are found to reveal the intrinsic mechanism of DNA damage repair.

Speaker Profile: Xu Yancong is a professor and doctoral supervisor at the College of Science, China Jiliang University. He holds a Ph.D. in Applied Mathematics from East China Normal University and was a postdoctoral fellow at Zhejiang University. He is the head of the mathematics discipline, the director of the Center for Mathematics and Interdisciplinary Research, a member of the American Society for Industrial and Applied Mathematics, a member of the American Mathematical Society, and a council member of the Zhejiang Mathematical and Physical Medicine Society. Director of the ZSMM Biomedical Mathematics Professional Committee of Zhejiang Province, selected as an outstanding young and middle-aged backbone teacher of Zhejiang Province, an outstanding teacher of Hangzhou City, and a member of the university's Outstanding Young and Middle-aged Support Program, etc. He/She has successively visited universities such as Brown University in the United States, University of Bremen in Germany, Kyoto University in Japan, York University in Canada, and The Hong Kong Polytechnic University. He/She has successively presided over the National Natural Science Foundation of China's general projects, Tianyuan Fund, Japan Global Center of Excellence (GCOE) projects, the Returned Overseas Study Fund, the Postdoctoral Fund, and the Zhejiang Provincial Natural Science Foundation, etc. At present, I am mainly engaged in theoretical and applied research on the branch of power systems. More than 60 academic papers have been published successively in journals such as DCDSA, Journal of Mathematical Biology, Journal of Nonlinear Science, Studies in Applied Mathematics, etc.