A SINGULAR BIOECONOMIC MODEL WITH DIFFUSION AND TIME DELAY  

作　　者：Qingling ZHANG Xue ZHANG Chao LIU 

机构地区：[1]Institute of Systems Science, Key Laboratory of Integrated Automation of Process Industry, Ministry of Edu-cation, Northeastern University, Shenyang 110004, China. [2]Department of Information and Computational Science Northeastern University at Qinhuangdao, Qinhuangdao066004, China.

出　　处：《Journal of Systems Science & Complexity》2011年第2期277-290,共14页系统科学与复杂性学报（英文版）

基　　金：This work was supported by the National Science Foundation of China under Grant No. 60974004 and Natural Science Foundation of China under Grant No. 60904009.

摘　　要：This paper studies a prey-predator singular bioeconomic system with time delay and diffusion, which is described by differential-algebraic equations. For this system without diffusion, there exist three bifurcation phenomena： Transcritical bifurcation, singularity induced bifurcation, and Hopf bifurcation. Compared with other biological systems described by differential equations, singularity induced bifurcation only occurs in singular system and usually links with the expansion of population. When the diffusion is present, it is shown that the positive equilibrium point loses its stability at some critical values of diffusion rate and periodic oscillations occur due to the increase of time delay. Furthermore, numerical simulations illustrate the effectiveness of results and the related biological implications are discussed.

关 键 词：DIFFUSION hopf bifurcation singular bioeconomic model singularity induced bifurcation time delay transcritical bifurcation. 

分 类 号：Q141[生物学—生态学] TM712[生物学—普通生物学]