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Article Dans Une Revue Comptes rendus de l'Académie des sciences. Série I, Mathématique Année : 2007

Liénard systems and potential-Hamiltonian decomposition III - Applications

Résumé

In the two previous Notes, we described the mathematical aspects of the potential-Hamiltonian (PH) decomposition, in particular for n-switches and Liénard systems. In the present Note, we give some examples of biological regulatory systems susceptible to be decomposed. We show that they can be modeled in terms of 2D-ODE belonging to n-switches and Liénard systems families. Although simplified, these models can be decomposed in a set of equations combining a potential and a Hamiltonian part. We discuss about the advantage of such a PH-decomposition for understanding the mechanisms involved in their regulatory abilities. We suggest a generalized algorithm to deal with differential systems having a second part of rational fraction type (frequently used in metabolic systems). Finally, we comment what can be interpreted as a precise signification in biological systems from the dynamical behaviors of both the potential and Hamiltonian parts.
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Dates et versions

hal-00211818 , version 1 (23-01-2008)

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  • HAL Id : hal-00211818 , version 1

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Nicolas Glade, Loïc Forest, Jacques Demongeot. Liénard systems and potential-Hamiltonian decomposition III - Applications. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2007, 344, pp 253-258. ⟨hal-00211818⟩
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