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
Periodic Solutions of Second Order Nonautonomous Systems with the Potentials Changing Sign
Some existence and multiplicity results for periodic solutions of second order nonautonomous systems with the potentials changing sign are presented. The proofs of the existence results rely on the use of a linking theorem and the Mountain Pass theorem by Ambrosetti and Rabinowitz [2]. The multiplicity results are deduced by the study of constrained critical points of minimum or Mountain Pass type.
Periodic solutions of some problems of 3-body type
Periodic Solutions on hypersurfaces and a result by C. Viterbo.
Periodic solutions with prescribed minimal period for convex autonomous hamiltonian systems.
Persistence of homoclinic tangencies for area-preserving maps