报告题目：Global Bifurcation Analysis of Polynomial Dynamical Systems
报 告 人：Valery A. Gaiko 白俄罗斯国家科学院
报告时间：2023年6月19日（星期一） 13:00-15:00
2023年6月20日（星期二） 15:35-16:35
2023年6月21日（星期三） 14:00-15:00
报告地点：2023年6月19日（星期一）海山楼A1101
2023年6月20日（星期二）海山楼B1410
D2023年6月21日（星期三）海山楼B1410
校内联系人：衣凤岐 教授 联系电话：84708351-8118
报告摘要： We consider polynomial dynamical systems and carry out a global bifurcation analysis of such systems. To control global bifurcations of limit cycles in planar systems, it is necessary to know the properties and combine the effects of all their rotation parameters. It can be done by means of the development of new bifurcation geometric methods based on the Wintner–Perko termination principle. Using these methods, we present, e. g., a solution of Hilbert’s Sixteenth Problem on the maximum number and distribution of limit cycles for quadratic systems, the Kukles cubic-linear system, the general Li´enard polynomial system with an arbitrary number of singular points, the Euler–Lagrange–Li´enard polynomial mechanical system, the FitzHugh–Nagumo neuronal system, Holling and Leslie–Gower systems which model the population dynamics in real ecological or biomedical systems, and a reduced planar quartic Topp system which models the dynamics of diabetes. Applying a similar approach, we study also three-dimensional polynomial dynamical systems and, in particular, complete the strange attractor bifurcation scenarios in Lorenz type systems connecting globally the homoclinic, period-doubling, Andronov–Shilnikov, and period-halving bifurcations of limit cycles.
报告人简介：V. Gaiko graduated from Kolosovskaya Secondary School in Stolbtsy-2 with a gold medal (1977) and Faculty of Mechanics and Mathematics, Belarusian State University with honors (1982); finished postgraduate studies at the Institute of Mathematics of the National Academy of Sciences of Belarus (1986) and postdoctoral studies at Belarusian State University of Informatics and Radioelectronics (1999). From 1987 to 2008, V. Gaiko had been working at the Department of Mathematics, BSUIR (assistant professor, associate professor, postdoctoral fellow). Since 2009, he is a leading researcher at the UIIP NAS of Belarus. Dr. Gaiko is an internationally recognized specialist in the qualitative theory of differential equations and the bifurcation theory of dynamical systems. He developed the global bifurcation theory of planar polynomial dynamical systems and solved Hilbert’s Sixteenth Problem for quadratic systems and Smale’s Thirteenth Problem for Liénard polynomial systems. Dr. Gaiko published over 400 scientific papers, including 3 monographs and over 100 articles in such well-known international journals as Nonlinear Analysis, Differential Equations and Dynamical Systems, International Journal of Dynamical Systems and Differential Equations, International Journal of Bifurcation and Chaos, Journal of Mathematical Sciences, Applied Mathematics Letters, Advances in Dynamical Systems and Applications, Cybernetics and Physics, Nonlinear Phenomena in Complex Systems. He made more than 350 reports at mathematical conferences and congresses, as well as seminars on the theory of differential equations and dynamical systems in leading international scientific centers in Austria, Belgium, Brazil, Bulgaria, China, Czech Republic, France, Germany, Great Britain, Hungary, India, Italy, Korea, Latvia, Lithuania, Netherlands, Norway, Poland, Slovakia, Spain, Sweden, USA, and CIS countries.
