Complex Dynamics Analysis of Generalized Tullock Contest  

作　　者：杨欣 周伟 YANG Xin;ZHOU Wei(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China

出　　处：《Journal of Donghua University(English Edition)》2023年第4期454-460,共7页东华大学学报（英文版）

基　　金：National Natural Science Foundation of China (No. 61863022);China Postdoctoral Science Foundation,China (No. 2017M623276)。

摘　　要：The generalized dynamic Tullock contest model with two homogeneous participants is established, in which both players have the same valuation of winning rewards and losing rewards. Firstly, the unique symmetric equilibrium point of the system is obtained by calculation and its local stability condition is given based on the Jury criterion. Then, two paths of the system from stability to chaos, namely flip bifurcation and Neimark-Sacker bifurcation, are analyzed by using the two-dimensional parametric bifurcation diagram. Meanwhile, the abundant Arnold tongues in the two-dimensional parametric bifurcation diagram are analyzed. Finally, the phenomenon of multistability of the system is illustrated through the basin of attraction, and the contact bifurcation occurs during the evolution of the basin of attraction with varying parameters.

关 键 词：Tullock contest Arnold tongue contact bifurcation chaos coexistence of attractor 

分 类 号：O225[理学—运筹学与控制论] O19[理学—数学]