中国物理B ›› 2001, Vol. 10 ›› Issue (10): 907-913.doi: 10.1088/1009-1963/10/10/305

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FREQUENCY CATASTROPHE AND CO-EXISTING ATTRACTORS IN A CELL Ca2+ NONLINEAR OSCILLATION MODEL WITH TIME DELAY

黄祖洽1, 应阳君2   

  1. (1)Institute of Low Energy Nuclear Physics, Beijing Normal University, Beijing 100875, China; (2)Institute of Low Energy Nuclear Physics, Beijing Normal University, Beijing 100875, China; Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • 收稿日期:2001-02-16 修回日期:2001-05-10 出版日期:2001-10-15 发布日期:2005-06-12
  • 基金资助:
    Project supported in part by the Doctoral Program Foundation of Institutions of Higher Education of China (Grant No. 98002713).

FREQUENCY CATASTROPHE AND CO-EXISTING ATTRACTORS IN A CELL Ca2+ NONLINEAR OSCILLATION MODEL WITH TIME DELAY

 Ying Yang-jun (应阳君)ab, Huang Zu-qia (黄祖洽)a   

  1. a Institute of Low Energy Nuclear Physics, Beijing Normal University, Beijing 100875, China; b Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • Received:2001-02-16 Revised:2001-05-10 Online:2001-10-15 Published:2005-06-12
  • Supported by:
    Project supported in part by the Doctoral Program Foundation of Institutions of Higher Education of China (Grant No. 98002713).

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摘要： Frequency catastrophe is found in a cell Ca2+ nonlinear oscillation model with time delay. The relation of the frequency transition to the time delay is studied by numerical simulations and theoretical analysis. There is a range of parameters in which two kinds of attractors with great frequency differences co-exist in the system. Along with parameter changes, a critical phenomenon occurs and the oscillation frequency changes greatly. This mechanism helps us to deepen the understanding of the complex dynamics of delay systems, and might be of some meaning in cell signalling.

Abstract: Frequency catastrophe is found in a cell Ca2+ nonlinear oscillation model with time delay. The relation of the frequency transition to the time delay is studied by numerical simulations and theoretical analysis. There is a range of parameters in which two kinds of attractors with great frequency differences co-exist in the system. Along with parameter changes, a critical phenomenon occurs and the oscillation frequency changes greatly. This mechanism helps us to deepen the understanding of the complex dynamics of delay systems, and might be of some meaning in cell signalling.

Key words: nonlinear dynamical system, delay differential equation, cell Ca2+, cellular signalling

中图分类号: 

  • 87.10.+y
02.60.-x (Numerical approximation and analysis) 05.45.-a (Nonlinear dynamics and chaos) 87.16.Uv (Active transport processes)