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A singular bioeconomic model with diffusion and time delay

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分类：Q141[生物学—生态学;生物学—普通生物学] TM712[电气工程—电力系统及自动化]
作者机构：[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.
相关基金：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.
相关项目：导数项系数矩阵具有不确定性的广义系统的鲁棒控制

关键词：奇异诱导分岔, 生物经济模型, 时间延迟, 扩散体, HOPF分岔, 微分代数方程, 经济体系, 分叉现象, Diffusion, hopf bifurcation, singular bioeconomic model, singularity induced bifurcation,time delay, transcritical bifurcation.

中文摘要：

这份报纸学习一个猎物食肉动物单个 bioeconomic 系统与预定延期和散开，它被微分代数学的方程描述。为没有散开的这个系统，在那里存在三分叉现象：Transcritical 分叉，奇特导致了分叉，和 Hopf 分叉。与微分方程描述的另外的生物系统相比，奇特仅仅导致了分叉在单个系统发生并且通常与人口的扩大连接。当散开是在场的时，积极平衡点在散开率的一些批评价值失去它的稳定性，这被显示出，周期的摆动由于时间延期的增加发生。而且，数字模拟说明结果和相关生物含意的有效性被讨论。

英文摘要：

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.