Liénard systems and potential-Hamiltonian decomposition II – algorithm
نویسندگان
چکیده
منابع مشابه
Liénard systems and potential-Hamiltonian decomposition: applications in biology.
In separated notes, we described the mathematical aspects of the potential-Hamiltonian (PH) decomposition, in particular, for n-switches and Liénard systems [J. Demongeot, N. Glade, L. Forest, Liénard systems and potential-Hamiltonian decomposition - I. Methodology, II. Algorithm and III. Applications, C. R. Acad. Sci., Paris, Ser. I, in press]. In the present note, we give some examples of bio...
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We show here how to approach with an increasing precision the limit-cycles of Liénard systems, bifurcating from a stable stationary state, by contour lines of Hamiltonian systems derived from a potential-Hamiltonian decomposition of the Liénard flow. We evoked in a previous Note the case (non polynomial) of pure potential systems (n-switches) and pure Hamiltonian systems (2D Lotka-Volterra), an...
متن کاملLiénard systems and potential-Hamiltonian decomposition I – methodology
Following the Hodge decomposition of regular vector fields we can decompose the second member of any Liénard system into 2 (non-unique) polynomials, the first corresponding to potential and the second to Hamiltonian dynamics. This polynomial Hodge decomposition is called potential-Hamiltonian, denoted PH-decomposition, and we give it for any polynomial differential system of dimension 2. We wil...
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In the two previous Notes, we described the mathematical aspects of the potential-Hamiltonian (PH) decomposition, in particular for n-switches and Liénard systems [1]. 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 system families [2]. Although simpl...
متن کاملSystèmes de Liénard et décomposition potentielle-Hamiltonienne - Applications en biologie Liénard systems and potential-Hamiltonian decomposition - Applications in biology
In separated notes, we described the mathematical aspects of the potential-Hamiltonian (PH) decomposition, in particular for n-switches and Liénard systems [1]. 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 ordinary differential equations belonging to n-switches and Liénard system familie...
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ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2007
ISSN: 1631-073X
DOI: 10.1016/j.crma.2006.10.013