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A qualitative mathematical model of the ontogeny of a circadian rhythm in crayfish

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Abstract

Based on experimental work on the ontogeny of the electroretinogram circadian rhythm in crayfish, we present a mathematical model simulating changes in both frequency and amplitude of the electroretinogram oscillation during several developmental stages until shortly before the adult age. Simultaneously, we propose a hypothetical oscillation in the hormonal release whose frequency is imposed on the electroretinogram oscillation. The model consists of two coupled nonlinear oscillators in which a dynamical response is obtained mainly through an Andronov-Hopf bifurcation. Through the construction of the model, a biological hypothesis about the essential elements underlying the ERG circadian rhythm and their interrelations is formulated and discussed.

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Authors and Affiliations

  1. Instituto de Matemáticas, UNAM, Apdo. Postal 70-637, 04511, México, D.F., México

    Miguel Lara-Aparicio & Santiago López de Medrano

  2. Departamento de Fisiología, División de Posgrado e Investigación, Facultad de Medicina, UNAM, 04510, México, D.F., México

    Beatriz Fuentes-Pardo & Enrique Moreno-Sáenz

Authors
  1. Miguel Lara-Aparicio
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  2. Santiago López de Medrano
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  3. Beatriz Fuentes-Pardo
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  4. Enrique Moreno-Sáenz
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Lara-Aparicio, M., de Medrano, S.L., Fuentes-Pardo, B. et al. A qualitative mathematical model of the ontogeny of a circadian rhythm in crayfish. Bltn Mathcal Biology 55, 97–110 (1993). https://doi.org/10.1007/BF02460296

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  • DOI: https://doi.org/10.1007/BF02460296

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