Oscillatory Activities in Regulatory Biological Networks and Hopf Bifurcation  

作　　者：晏世伟 王祺 射柏松 张丰收 

机构地区：[1]The Key Laboratory of Beam Technology and Material Modification of Ministry of Education, Institute of Low Energy Nuclear Physics, Beijing Normal University, Beijing 100875 [2]Center of Theoretical Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000 [3]Beijing Radiation Center, Belling 100875

出　　处：《Chinese Physics Letters》2007年第6期1771-1774,共4页中国物理快报（英文版）

基　　金：Supported by the National Natural Science Foundation of China under Grant Nos 10475008 and 10435020, the Scientific Research Foundation for the Returned 0verseas Chinese Scholars, Ministry of Personnel of China under Grant No M0P2006138, the Ministry of Education of China under Grant No 2005383, the Foundations for Excellent Scientists of Beijing under Grant No 20041D1300120.

摘　　要：Exploiting the nonlinear dynamics in the negative feedback loop, we propose a statistical signal-response model to describe the different oscillatory behaviour in a biological network motif. By choosing the delay as a bifurcation parameter, we discuss the existence of Hopf bifurcation and the stability of the periodic solutions of model equations with the centre manifold theorem and the normal form theory. It is shown that a periodic solution is born in a Hopf bifurcation beyond a critical time delay, and thus the bifurcation phenomenon may be important to elucidate the mechanism of oscillatory activities in regulatory biological networks.Exploiting the nonlinear dynamics in the negative feedback loop, we propose a statistical signal-response model to describe the different oscillatory behaviour in a biological network motif. By choosing the delay as a bifurcation parameter, we discuss the existence of Hopf bifurcation and the stability of the periodic solutions of model equations with the centre manifold theorem and the normal form theory. It is shown that a periodic solution is born in a Hopf bifurcation beyond a critical time delay, and thus the bifurcation phenomenon may be important to elucidate the mechanism of oscillatory activities in regulatory biological networks.

关 键 词：P53-MDM2 INTERACTION P53 CELLS TIME MDM2 EXPRESSION MODEL 

分 类 号：O3[理学—力学]