Oscillatory Activities in Regulatory Biological Networks and Hopf Bifurcation
YAN Shi-Wei 1,2,3, WANG Qi1, XIE Bai-Song 1,3, ZHANG Feng-Shou 1,2,3
1The Key Laboratory of Beam Technology and Material Modification of Ministry of Education, Institute of Low Energy Nuclear Physics, Beijing Normal University,Beijing 1008752Center of Theoretical Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 7300003Beijing Radiation Center, Beijing 100875
Oscillatory Activities in Regulatory Biological Networks and Hopf Bifurcation
YAN Shi-Wei 1,2,3;WANG Qi1;XIE Bai-Song 1,3;ZHANG Feng-Shou 1,2,3
1The Key Laboratory of Beam Technology and Material Modification of Ministry of Education, Institute of Low Energy Nuclear Physics, Beijing Normal University,Beijing 1008752Center of Theoretical Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 7300003Beijing Radiation Center, Beijing 100875
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.
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2007, Vol. 24 
