24 research outputs found
Synchronization of stochastic hybrid oscillators driven by a common switching environment
Many systems in biology, physics and chemistry can be modeled through
ordinary differential equations, which are piecewise smooth, but switch between
different states according to a Markov jump process. In the fast switching
limit, the dynamics converges to a deterministic ODE. In this paper we suppose
that this limit ODE supports a stable limit cycle. We demonstrate that a set of
such oscillators can synchronize when they are uncoupled, but they share the
same switching Markov jump process. The latter is taken to represent the effect
of a common randomly switching environment. We determine the leading order of
the Lyapunov coefficient governing the rate of decay of the phase difference in
the fast switching limit. The analysis bears some similarities to the classical
analysis of synchronization of stochastic oscillators subject to common white
noise. However the discrete nature of the Markov jump process raises some
difficulties: in fact we find that the Lyapunov coefficient from the
quasi-steady-state approximation differs from the Lyapunov coefficient one
obtains from a second order perturbation expansion in the waiting time between
jumps. Finally, we demonstrate synchronization numerically in the radial
isochron clock model and show that the latter Lyapinov exponent is more
accurate
On Implicit Finite-Time and Fixed-Time ISS Lyapunov Functions
International audienceThis article presents a theoretical framework to study finite-time and fixed-time input-to-state stability of non-linear systems using the implicit Lyapunov function formulation. This approach allows to determine stability, robustness and convergence type of a given system without relying in an explicit Lyapunov function
Fast robust control of linear systems subject to actuator saturation
This paper deals with the robust stability of soft variable-structure controls. More precisely, the control of linear plants subject to parametric uncertainty and actuator saturation is considered. Earlier works are summarized and new results are presented in this paper. It is shown that for all considered types of soft variable-structure controls, the robustness analysis leads to parameter-dependent Lyapunov inequalities. An overhead crane control is given as an illustrating example
Orbitally symmetric systems with applications to planar centers
We present a generalization of the most usual symmetries in differential equations known as the time-reversibility and the equivariance ones. We check that the typical properties are also valid for the new definition that unifies both. With it, we are able to present new families of planar polynomial vector fields having equilibrium points of center type. Moreover, we provide the highest lower bound for the local cyclicity of an equilibrium point of polynomial vector fields of degree 6, M(6) ≥ 48
Gravitational Ionization: Periodic Orbits of Binary Systems Perturbed by Gravitational Radiation
The long term perturbation of a Newtonian binary system by an incident
gravitational wave is discussed in connection with the issue of gravitational
ionization. The periodic orbits of the planar tidal equation are investigated
and the conditions for their existence are presented. The possibility of
ionization of a Keplerian orbit via gravitational radiation is discussed.Comment: ps file, 35 page
Rendiconti dell'Istituto di Matematica dell'Università di Trieste. An International Journal of Mathematics. Vol. 44 (2012)
Rendiconti dell’Istituto di Matematica dell’Università di Trieste was founded in 1969 by Arno Predonzan, with the aim of publishing original research articles in all fields of mathematics and has been the first Italian mathematical journal to be published also on-line. The access to the electronic version of the journal is free. All published articles are available on-line. The journal can be obtained by subscription, or by reciprocity with other similar journals. Currently more than 100 exchange agreements with mathematics departments and institutes around the world have been entered in
Hydrodynamic synchronization of flagellar oscillators
We survey the theory synchronization in collections of noisy oscillators.
This framework is applied to flagellar synchronization by hydrodynamic
interactions. The time-reversibility of hydrodynamics at low Reynolds numbers
prompts swimming strokes that break symmetry to facilitate hydrodynamic
synchronization. We discuss different physical mechanisms for flagellar
synchronization, which break this symmetry in different ways.Comment: 15 pages, 3 figures; accepted for publication in EPJ Special Topics
Issue,Lecture Notes of the Summer School "Microswimmers -- From Single
Particle Motion to Collective Behaviour'', organised by the DFG Priority
Programme SPP 1726 (Forschungszentrum J\"ulich, J\"ulich, 2015
New lower bounds for the Hilbert numbers using reversible centers
Altres ajuts: UNAB13-4E-1604 (FEDER)In this paper we provide the best lower bounds, that are known up to now, for the Hilbert numbers of polynomial vector fields of degree N,, for small values of N. These limit cycles appear bifurcating from symmetric Darboux reversible centers with very high simultaneous cyclicity. The considered systems have, at least, three centers, one on the reversibility straight line and two symmetric outside it. More concretely, the limit cycles are in a three nests configuration and the total number of limit cycles is at least 2n + m, for some values of n and m. The new lower bounds are obtained using simultaneous degenerate Hopf bifurcations. In particular, H(4) ≥ 28, H(5) ≥ 37, H(6) ≥ 53, H(7) ≥ 74, H(8) ≥ 96, H(9) ≥ 120 and H(10) ≥ 142
Zwei-Freiheitsgrade-Regelung linearer Systeme mit Stellgrößen- und Stellratenbegrenzungen
In diesem Artikel wird eine schnelle
Führungsregelung für lineare Regelstrecken unter Stellgrößenund Stellratenbeschränkungen vorgestellt. Dazu wird ein
auch für nichtlineare Systeme anwendbarer inversionsbasierter Vorsteuerungsentwurf mit einem weich-strukturvariablen
Regler kombiniert. Die Formulierung eines konvexen Optimierungsproblems erlaubt den effizienten Reglerentwurf