Systèmes de Liénard et décomposition potentielle-Hamiltonienne II - Algorithme Liénard systems and potential-Hamiltonian decomposition II - Algorithm

Abstract

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), and here we show that, with the proposed approximation, we can deal with the case of mixed systems (van der Pol or FitzHugh-Nagumo) frequently used for modelling oscillatory systems in biology. We suggest finally that the proposed algorithm, generic for PHdecomposition, can be used for estimating the isochronal fibration in some specific cases near the pure potential or Hamiltonian systems. In a following Note, we will give applications in biology of the potential-Hamiltonian decomposition.

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Cite this paper

@inproceedings{Demongeot1968SystemesDL, title={Systèmes de Liénard et décomposition potentielle-Hamiltonienne II - Algorithme Liénard systems and potential-Hamiltonian decomposition II - Algorithm}, author={Jacques Demongeot and Nicolas Glade and Lo{\"{i}c Forest}, year={1968} }