A mathematical model of suspension bridges
We prove the existence of weak T-periodic solutions for a nonlinear mathematical model associated with suspension bridges. Under further assumptions a regularity result is also given.
A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems.
A note on generic chaos
We consider dynamical systems on a separable metric space containing at least two points. It is proved that weak topological mixing implies generic chaos, but the converse is false. As an application, some results of Piórek are simply reproved.
A Note on Shock Profiles in Dissipative Hyperbolic and Parabolic Models
A realistic exponential estimate for a paradigm hamiltonian
A stability criterion for periodic systems with first integrals
A variational approach to chaotic dynamics in periodically forced nonlinear oscillators
A variational construction of chaotic trajectories for a Hamiltonian system on a torus
A geometric criterion for the existence of chaotic trajectories of a Hamiltonian system with two degrees of freedom and the configuration space a torus is given. As an application, positive topological entropy is established for a double pendulum problem.
Adaptive finite-time generalized outer synchronization between two different dimensional chaotic systems with noise perturbation
This paper is further concerned with the finite-time generalized outer synchronization between two different dimensional chaotic systems with noise perturbation via an adaptive controller. First of all, we introduce the definition of finite-time generalized outer synchronization between two different dimensional chaotic systems. Then, employing the finite-time stability theory, we design an adaptive feedback controller to realize the generalized outer synchronization between two different dimensional...
Analysis of a Population Model Structured by the Cells Molecular Content
We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak assumptions, and deduce from it the long-time convergence. The main difficulty comes from natural degeneracy of birth terms that we overcome with a regularization technique. We then extend the results to the case with several parameters and recall the link between this...
Angenäherte Schwingungsfrequenzformeln für konservative Systeme (4)
Application of a center manifold theory to a reaction-diffusion system of collective motion of camphor disks and boats
Unidirectional motion along an annular water channel can be observed in an experiment even with only one camphor disk or boat. Moreover, the collective motion of camphor disks or boats in the water channel exhibits a homogeneous and an inhomogeneous state, depending on the number of disks or boats, which looks like a kind of bifurcation phenomena. In a theoretical research, the unidirectional motion is represented by a traveling wave solution in a model. Hence it suffices to investigate a linearized...
Asymptotic behaviour of the solvability set for pendulum-type equations with linear damping and homogeneous Dirichlet conditions.
Asymptotic stability for perturbed hamiltonian systems, II
Autoparametric vibrations of a nonlinear system with pendulum.