Lecture Content：

In this talk, we introduce a discrete model with periodic parameters to depict the Wolbachia spread dynamics in mosquito populations in cyclic environments. This work modifies the models established in the existing literature that did not take into account the variation of parameters with environmental periodic changes due to seasonality and other factors. When the parameters in our model are constants, it has been extensively studied and widely used.  We present a conjecture about the existence of at most two periodic solutions worthy of further study, and show that the conjecture is true for the special case of 2-periodic parameters.  Numerical simulations are also provided to illustrate the occurrence of periodic phenomena.

Speaker Introduction:

Professor Yu Jianshe, a distinguished expert and doctoral supervisor, is the recipient of the National Science Fund for Distinguished Young Scholars and has been recognized as a middle-aged expert with outstanding contributions at the national level. He is also a National Labor Model in the education system and has been selected for the first and second tiers of the "Millions of Talents Project" by the National Government. A recipient of the Cross-Century Excellent Talent Award from the Ministry of Education and enjoying government special allowances, he currently serves as the Director of the Applied Mathematics Research Center at Guangzhou University. Previously, he held positions as Vice-President of Hunan University and President and Party Secretary of Guangzhou University. He has led over 10 major research projects funded by the National Natural Science Foundation of China, including the Distinguished Young Scholars Fund and various other grants. His research focuses on the theoretical and practical applications of differential equations in dynamical systems, difference equations, and biomathematical models. He has published over 100 papers in leading international journals, including Nature, Journal of Differential Equations, SIAM Journal on Applied Mathematics, Journal of Mathematical Biology, and Journal of Theoretical Biology.