A singular bioeconomic model with diffusion and time delay

被引：0
作者：
Qingling Zhang
Xue Zhang
Chao Liu
机构：
[1] Northeastern University,Institute of Systems Science, Key Laboratory of Integrated Automation of Process Industry, Ministry of Education
[2] Department of Information and Computational Science Northeastern University at Qinhuangdao,undefined
来源：
Journal of Systems Science and Complexity | 2011年 / 24卷
关键词：
Diffusion; hopf bifurcation; singular bioeconomic model; singularity induced bifurcation; time delay; transcritical bifurcation;
D O I：
暂无
中图分类号：
学科分类号：
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.
引用
收藏
页码：277 / 290
页数：13
相关论文
共 38 条
  • [1] Ayasun S.(2004)Computation of singular and singularity induced bifurcation points of differential-algebraic power system model IEEE Transaction on Circuits and Systems-I: Fundamental Theory and Applications 51 1525-1538
  • [2] Nwankpa C. O.(2005)Singularity-induced bifurcations in lumped circuits IEEE Transaction on Circuits and Systems-I: Fundamental Theory and Applications 52 1442-1450
  • [3] Kwatny H. G.(2006)On the observability of linear differentialalgebraic systems with delays IEEE Transactions on Automatic Control 51 1387-1392
  • [4] Riaza R.(1999)Global searching ability of chaotic neural networks IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 46 974-993
  • [5] Marchenko V.M.(1996)Modeling the complexity of genetic networks: Understanding multigenic and pleiotropic regulation Complexity 1 45-63
  • [6] Poddubnaya O. N.(1954)Economic theory of a common property resource: The fishery Journal of Political Economy 63 116-124
  • [7] Zaczkiewicz Z.(2008)Positive periodic solution for a semi-ratio-dependent predator-prey system with diffusion and time delays Nonlinear Analysis: Real World Applications 9 239-249
  • [8] Chen L. N.(2008)Analysis of nonautonomous predator-prey model with nonlinear diffusion and time delay Applied Mathematics and Computation 196 129-136
  • [9] Aihara K.(2004)Positive periodic solution of two-species ratio-dependent predator-prey system with time delay in two-patch environment Applied Mathematics and Computation 150 737-748
  • [10] Somogyi R.(2006)Permanence and extinction in nonlinear single and multiple species system with diffusion Applied Mathematics and Computation 177 410-426
1234