Oscillatory activities in regulatory biological networks and Hopf bifurcation

作者：Yan Shi Wei^*; Wang Qi; Xie Bai Song; Zhang Feng Shou

来源：Chinese Physics Letters, 2007, 24(6): 1771-1774.

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.

• 出版日期2007-6
• 单位北京师范大学; 北京市辐射中心