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Compact set valued flows: Applications in biological modelling

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Abstract

Compact set valued iterations generalize classical point iterations quite naturally by replacing the function f with a tube f in the discrete iterations equation. In Section 3, some bifurcation results about logistic tube iterations are given. In Section 4, an analogous dynamical behaviour for the phase response tube involved in the entrainment of the respiratory rhythm is studied.

Resume

Les itérations à valeurs compactes constituent une généralisation naturelle des itérations ponctuelles classiques, dans lesquelles on remplace la function f à itérer par un tube fonctionnel f. Nous donnons, dans la Section 3, des résultats concernant les bifurcations des itérations d'un tube logistique et, dans le Section 4, nous étudions un exemple comparable d'itérations apparaissant daps l'entraînement du rythme respiratoire.

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Authors
  1. Jacques Demongeot
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  2. Paul Kulesal
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  3. James Muffay
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Additional information

present address: Department of Applied Mathematics, FS-20, University of Washington, Seattle WA 98 195, USA

permanent address: TIMC-IMAG, Université J. Fourier de Grenoble, 38 700 La Tronche, France

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Demongeot, J., Kulesal, P. & Muffay, J. Compact set valued flows: Applications in biological modelling. Acta Biotheor 44, 349–358 (1996). https://doi.org/10.1007/BF00046538

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  • DOI: https://doi.org/10.1007/BF00046538

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