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.
Origine | Fichiers éditeurs autorisés sur une archive ouverte |
---|