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Invariant tori in the Sun--Jupiter--Saturn system
Qualitative behavior of a family of delay-differential models of the Glucose-Insulin system
| 1. | CNR-IASI, BioMatLab, UCSC - Largo A., Gemelli 8, 00168 Roma, Italy |
| 2. | Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti", Consiglio Nazionale delle Ricerche (IASI-CNR), BioMatLab - UCSC - Largo A. Gemelli 8, 00168 Roma, Italy, Italy |
Local stability is investigated in a pair of interesting member models: one, a discrete-delays differential system; the other, a distributed-delay system reducing to an ordinary differential system evolving on a suitably defined extended state space. In both cases conditions are given on the physical parameters in order to ensure the local asymptotic stability of the equilibrium point. These conditions are always satisfied, given the actual parameter estimates obtained experimentally. A study of the global stability properties is performed, but while from simulations it could be conjectured that the models considered are globally asymptotically stable, sufficient stability criteria, formally derived, are not actually satisfied for physiological parameters values. Given the practical importance of the models studied, further analytical work may be of interest to conclusively characterize their behavior.
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