Title

Multistability, oscillations and bifurcations in feedback loops.

SelectedWorks Author Profiles:

Maria Conceição A. Leite

Document Type

Article

Publication Date

2010

ISSN

1551-0018

Abstract

Feedback loops are found to be important network structures in regulatory networks of biological signaling systems because they are responsible for maintaining normal cellular activity. Recently, the functions of feedback loops have received extensive attention. The existing results in the literature mainly focus on verifying that negative feedback loops are responsible for oscillations, positive feedback loops for multistability, and coupled feedback loops for the combined dynamics observed in their individual loops. In this work, we develop a general framework for studying systematically functions of feedback loops networks. We investigate the general dynamics of all networks with one to three nodes and one to two feedback loops. Interestingly, our results are consistent with Thomas' conjectures although we assume each node in the network undergoes a decay, which corresponds to a negative loop in Thomas' setting. Besides studying how network structures influence dynamics at the linear level, we explore the possibility of network structures having impact on the nonlinear dynamical behavior by using Lyapunov-Schmidt reduction and singularity theory.

Comments

Abstract only. Published in Mathematical Biosciences and Engineering, 7(1), 83-97. doi:10.3934/mbe.2010.7.83.

Publisher

American Institute of Mathematical Sciences (AIMS Press)

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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