CODIMENSION-TWO BIFURCATIONS ANALYSIS AND TRACKING CONTROL ON A DISCRETE EPIDEMIC MODEL  

作　　者：Na YI Qingling ZHANG Peng LIU Yanping LIN 

机构地区：[1] Institute of Systems Science, Northeastern University, Shenyang 110004, China [2] School of Sciences, Liaoning Shihua University, Fushun 113001, China [3] School of Management, Shenyang University of Technology, Shenyang 110870, China [4] Department of Mathematics, The Hong Kong Polytechnic University, Hong Kong, China

出　　处：《Journal of Systems Science & Complexity》2011年第6期1033-1056,共24页系统科学与复杂性学报（英文版）

基　　金：This research is supported by the National Natural Science Foundation of China under Grant Nos. 60974004 and 71001074, and the Science Research Foundation of Department of Education of Liaoning Province of China under Grant No. W2010302.

摘　　要：In this paper, the dynamic behaviors of a discrete epidemic model with a nonlinear incidence rate obtained by Euler method are discussed, which can exhibit the periodic motions and chaotic behaviors under the suitable system parameter conditions. Codimension-two bifurcations of the discrete epidemic model, associated with 1：1 strong resonance, 1：2 strong resonance, 1：3 strong resonance and 1：4 strong resonance, are analyzed by using the bifurcation theorem and the normal form method of maps. Moreover, in order to eliminate the chaotic behavior of the discrete epidemic model, a tracking controller is designed such that the disease disappears gradually. Finally, numerical simulations are obtained by the phase portraits, the maximum Lyapunov exponents diagrams for two different varying parameters in 3-dimension space, the bifurcation diagrams, the computations of Lyapunov exponents and the dynamic response. They not only illustrate the validity of the proposed results, but also display the interesting and complex dynamical behaviors.

关 键 词：CHAOS codimension-two bifurcations discrete epidemic model tracking control. 

分 类 号：O175.1[理学—数学] O32[理学—基础数学]