Oscillations in multi-stable monotone systems with slowly varying feedback

Tomáš Gedeon; Eduardo D. Sontag

doi:https://doi.org/10.1016/j.jde.2007.05.029

Oscillations in multi-stable monotone systems with slowly varying feedback

Tomáš Gedeon, Eduardo D. Sontag

Rutgers, The State University

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A useful approach to the study of these complex systems is to view them as decomposed into feedback loops around open loop monotone systems. Key features of the dynamics of the original system are then deduced from the input-output characteristics of the open loop system and the sign of the feedback. This paper extends these results, showing how to use the same framework of input-output systems in order to prove existence of oscillations, if the slowly varying strength of the feedback depends on the state of the system.

Original language	American English
Pages (from-to)	273-295
Number of pages	23
Journal	Journal of Differential Equations
Volume	239
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2007.05.029
State	Published - Aug 15 2007

ASJC Scopus subject areas

Analysis
Applied Mathematics

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title = "Oscillations in multi-stable monotone systems with slowly varying feedback",

abstract = "The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A useful approach to the study of these complex systems is to view them as decomposed into feedback loops around open loop monotone systems. Key features of the dynamics of the original system are then deduced from the input-output characteristics of the open loop system and the sign of the feedback. This paper extends these results, showing how to use the same framework of input-output systems in order to prove existence of oscillations, if the slowly varying strength of the feedback depends on the state of the system.",

author = "Tom{\'a}{\v s} Gedeon and Sontag, {Eduardo D.}",

note = "Funding Information: * Corresponding author. E-mail address: gedeon@math.montana.edu (T. Gedeon). 1 This research is partially supported by grants NSF EIA-BITS-42611, NIH-NCRR P20 RR16455-04 and DMS/NIH-4W0467. 2 This research is partially supported by grants NSF DMS-0614371 and NSF DMS-0504557.",

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T1 - Oscillations in multi-stable monotone systems with slowly varying feedback

AU - Gedeon, Tomáš

AU - Sontag, Eduardo D.

N1 - Funding Information: * Corresponding author. E-mail address: gedeon@math.montana.edu (T. Gedeon). 1 This research is partially supported by grants NSF EIA-BITS-42611, NIH-NCRR P20 RR16455-04 and DMS/NIH-4W0467. 2 This research is partially supported by grants NSF DMS-0614371 and NSF DMS-0504557.

PY - 2007/8/15

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N2 - The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A useful approach to the study of these complex systems is to view them as decomposed into feedback loops around open loop monotone systems. Key features of the dynamics of the original system are then deduced from the input-output characteristics of the open loop system and the sign of the feedback. This paper extends these results, showing how to use the same framework of input-output systems in order to prove existence of oscillations, if the slowly varying strength of the feedback depends on the state of the system.

AB - The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A useful approach to the study of these complex systems is to view them as decomposed into feedback loops around open loop monotone systems. Key features of the dynamics of the original system are then deduced from the input-output characteristics of the open loop system and the sign of the feedback. This paper extends these results, showing how to use the same framework of input-output systems in order to prove existence of oscillations, if the slowly varying strength of the feedback depends on the state of the system.

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JO - Journal of Differential Equations

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Oscillations in multi-stable monotone systems with slowly varying feedback

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