Bifurcation of Transition Paths Induced by Coupled Bistable Systems

We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example, and show that its transition paths are bifurcating. We then derive a criterion to predict the bifurcat...

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Bibliographic Details
Published inarXiv.org
Main Authors Tian, Chengzhe, Mitarai, Namiko
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.05.2016
Subjects
Bifurcations
Circuits
Computer simulation
Mathematical models
Physics - Biological Physics
Physics - Chaotic Dynamics
Potential energy
Quantitative Biology - Molecular Networks
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Summary:We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example, and show that its transition paths are bifurcating. We then derive a criterion to predict the bifurcation of transition paths in a generalized coupled bistable system. We confirm the validity of the theory for the example system by numerical simulation. We also demonstrate in the example system that, if the steady states of individual gene circuits are not changed by the coupling, the bifurcation pattern is not dependent on the number of gene circuits. We further show that the transition rate exponentially decreases with the number of gene circuits when the transition path does not bifurcate, while a bifurcation facilitates the transition by lowering the quasi-potential energy barrier.
ISSN:2331-8422
DOI:10.48550/arxiv.1603.04477