Pierre Coullet

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We study the resonance at zero frequency in presence of a neutral mode in quasi-reversible systems. The asymptotic normal form is derived and it is shown that in the presence of a reflection symmetry it is equivalent to the set of real Lorenz equations. Near the critical point an analytical condition for the persistence of an homoclinic curve is calculated(More)
For the particular case of an excitable FitzHugh-Nagumo system with diffusion, we investigate the transition from annihilation to crossing of the waves in the head-on collision. The analysis exploits the similarity between the local and the global phase portraits of the system. We find that the transition has features typical of the nucleation theory of(More)
We propose a simple model for the chaotic dripping of a faucet in terms of a return map constructed by analyzing the stability of a pendant drop. The return map couples two classical normal forms, an Andronov saddle-node bifurcation, and a Shilnikov homoclinic bi-furcation. The former corresponds to the initiation of the instability when the drop volume(More)
We analyze the transition from annihilation to preservation of colliding waves. The analysis exploits the similarity between the local and global phase portraits of the system. The transition is shown to be the infinite-dimensional analog of the creation and annihilation of limit cycles in the plane via a homo-clinic Andronov bifurcation, and has parallels(More)
Conductance-based (CB) models are a class of high dimensional dynamical systems derived from biophysical principles to describe in detail the electrical dynamics of single neurons. Despite the high dimensionality of these models, the dynamics observed for realistic parameter values is generically planar and can be minimally described by two equations. In(More)
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