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- Title
A mathematical model of circadian rhythms synchronization using fractional differential equations system of coupled van der Pol oscillators.
- Authors
Escalante-Martínez, J. E.; Gómez-Aguilar, J. F.; Calderón-Ramón, C.; Aguilar-Meléndez, A.; Padilla-Longoria, P.
- Abstract
This paper presents an alternative representation of a system of differential equations qualitatively showing the behavior of the biological rhythm of a crayfish during their transition from juvenile to adult stages. The model focuses on the interaction of four cellular oscillators coupled by diffusion of a hormone, a parameter is used to simulate the quality of communication among the oscillators, in biological terms, it measures developmental maturity of the crayfish. Since some quorum-sensing mechanism is assumed to be responsible for the synchronization of the biological oscillators, it is natural to investigate the possibility that the underlying diffusion process is not standard, i.e. it may be a so-called anomalous diffusion. In this case, it is well understood that diffusion equations with fractional derivatives describe these processes in a more realistic way. The alternative formulation of these equations contains fractional operators of Liouville-Caputo and Caputo-Fabrizio type. The numerical simulations of the equations reflect synchronization of ultradian rhythms leading to a circadian rhythm. The classical behavior is recovered when the order of the fractional derivative is . We discuss possible biological implications.
- Subjects
CIRCADIAN rhythms; MATHEMATICAL models; FRACTIONAL differential equations; VAN der Pol oscillators (Physics); BIOLOGICAL rhythms; CRAYFISH
- Publication
International Journal of Biomathematics, 2018, Vol 11, Issue 1, p-1
- ISSN
1793-5245
- Publication type
Article
- DOI
10.1142/S1793524518500146