A singular bioeconomic model with diffusion and time delay

作者：Zhang Qingling^*; Zhang Xue; Liu Chao

来源：Journal of Systems Science and Complexity, 2011, 24(2): 277-290.

DOI：10.1007/s11424-010-8067-z

• Diffusion
• hopf bifurcation
• singular bioeconomic model
• singularity induced bifurcation
• time delay
• transcritical bifurcation

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.

• 出版日期2011-4
• 单位东北大学