Orbites Hétérocliniques au Voisinage d'une Bifurcation de Poincaré Dégénérée pour les Champs de Vecteurs de ...
Orbites périodiques de systèmes conservatifs
Orbites périodiques des systèmes hamiltoniens autonomes
Orbites périodiques des systèmes hamiltoniens du type de celui des trois corps
Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches
This work contributes to classify the dynamic behaviors of piecewise smooth systems in which border collision bifurcations characterize the qualitative changes in the dynamics. A central point of our investigation is the intersection of two border collision bifurcation curves in a parameter plane. This problem is also associated with the continuity breaking in a fixed point of a piecewise smooth map. We will relax the hypothesis needed in [4] where...
Parametrically excited nonlinear systems: A comparison of two methods.
Path formulation for a modal family.
Path formulation for multiparameter -equivariant bifurcation problems
We implement a singularity theory approach, the path formulation, to classify -equivariant bifurcation problems of corank 2, with one or two distinguished parameters, and their perturbations. The bifurcation diagrams are identified with sections over paths in the parameter space of a -miniversal unfolding of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of onto its unfolding parameter space. We apply our results to degenerate...
Pattern Formation of Competing Microorganisms in Sediments
We present a three species model describing the degradation of substrate by two competing populations of microorganisms in a marine sediment. Considering diffusion to be the main transport process, we obtain a reaction diffusion system (RDS) which we study in terms of spontaneous pattern formation. We find that the conditions for patterns to evolve are likely to be fulfilled in the sediment. Additionally, we present simulations that are consistent with experimental data from the literature. We...
Period doubling bifurcations in a two-box model of the Brusselator
Two theorems about period doubling bifurcations are proved. A special case, where one multiplier of the homogeneous solution is equal to +1 is discussed in the Appendix.
Periodic and heteroclinic orbits for a periodic hamiltonian system
Periodic bounce trajectories with a low number of bounce points
Periodic orbits of maps with an infinite number of partition points.
Periodic orbits of renormalisation for the correlations of strange nonchaotic attractors.
Periodic points of linked twist mappings
Periodic solutions near an equilibrium of a differential equation with a first integral
Periodic solutions of a non coercive Hamiltonian system.
Periodic Solutions of Hamiltonian Systems on Hypersurfaces in Torus.
Periodic solutions of non-autonomous Hamiltonian systems with symmetries.
Periodic solutions of second order hamiltonian systems bifurcating from infinity