Graphical and Analytic Criteria for the Existence of Protein Level Oscillations in Cyclic Gene Regulatory Networks
- Authors
- Hori, Yutaka; Kim, Tae-Hyoung; Hara, Shinji
- Issue Date
- 2009
- Publisher
- IEEE
- Citation
- PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009), pp 3521 - 3526
- Pages
- 6
- Journal Title
- PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009)
- Start Page
- 3521
- End Page
- 3526
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/52289
- DOI
- 10.1109/CDC.2009.5400718
- ISSN
- 0743-1546
- Abstract
- This paper investigates the criteria for the existence of protein level oscillations in a class of gene regulatory networks, where a nonlinear differential equation model is considered to analyze its dynamical behavior. There are two steps to derive such criteria: We first employ a Poincare-Bendixson type theorem to restrict the class of solution trajectories, and then carry out a local stability analysis of linearized systems with a generalized frequency variable. Then, our main results, graphical and its equivalent analytic criteria which are easily applicable for the networks consisting of arbitrary number of genes, are derived. Their distinctive features are also verified through numerical simulations.
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