Mathematical Biosciences and Engineering, 2014, 11(2): 317-330. doi: 10.3934/mbe.2014.11.317.

Primary: 92B25, 34C15; Secondary: 68U20.

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Modeling some properties of circadian rhythms

1. Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México,
2. Laboratorio de Cronobiología, Departamento de Fisiología, Facultad de Medicina, Universidad Nacional Autónoma de México
3. Departamento de Matemáticas y Mecánica, Instituto de Investigaciones, en Matemáticas Aplicadas y en Sistemas. Universidad Nacional Autónoma de México

Mathematical models have been very useful in biological research. From theinteraction of biology and mathematics, new problems have emerged that havegenerated advances in the theory, suggested further experimental work andmotivated plausible conjectures. From our perspective, it is absolutelynecessary to incorporate modeling tools in the study of circadian rhythmsand that without a solid mathematical framework a real understanding of themwill not be possible. Our interest is to study the main process underlyingthe synchronization in the pacemaker of a circadian system: thesemechanisms should be conserved in all living beings. Indeed, from anevolutionary perspective, it seems reasonable to assume that either theyhave a common origin or that they emerge from similar selectioncircumstances. We propose a general framework to understand the emergence ofsynchronization as a robust characteristic of some cooperative systems ofnon-linear coupled oscillators. In a first approximation to the problem wevary the topology of the network and the strength of the interactions amongoscillators. In order to study the emergent dynamics, we carried out somenumerical computations. The results are consistent with experiments reportedin the literature. Finally, we proposed a theoretical framework to study thephenomenon of synchronization in the context of circadian rhythms: thedissipative synchronization of nonautonomous dynamical systems.
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Keywords circadian rhythms; network architecture.; cooperative networks; Synchronization; ultradian rhythms

Citation: Miguel Lara-Aparicio, Carolina Barriga-Montoya, Pablo Padilla-Longoria, Beatriz Fuentes-Pardo. Modeling some properties of circadian rhythms. Mathematical Biosciences and Engineering, 2014, 11(2): 317-330. doi: 10.3934/mbe.2014.11.317

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