688 research outputs found
Linearization of analytic and non--analytic germs of diffeomorphisms of
We study Siegel's center problem on the linearization of germs of
diffeomorphisms in one variable. In addition of the classical problems of
formal and analytic linearization, we give sufficient conditions for the
linearization to belong to some algebras of ultradifferentiable germs closed
under composition and derivation, including Gevrey classes.
In the analytic case we give a positive answer to a question of J.-C. Yoccoz
on the optimality of the estimates obtained by the classical majorant series
method.
In the ultradifferentiable case we prove that the Brjuno condition is
sufficient for the linearization to belong to the same class of the germ. If
one allows the linearization to be less regular than the germ one finds new
arithmetical conditions, weaker than the Brjuno condition. We briefly discuss
the optimality of our results.Comment: AMS-Latex2e, 11 pages, in press Bulletin Societe Mathematique de
Franc
The Stochastic Evolution of a Protocell: The Gillespie Algorithm in a Dynamically Varying Volume
We propose an improvement of the Gillespie
algorithm allowing us to study the time evolution of an ensemble of chemical
reactions occurring in a varying volume, whose growth is directly related to
the amount of some specific molecules, belonging to the reactions set.
This allows us to study the stochastic evolution of a protocell, whose volume
increases because of the production of container molecules. Several protocell
models are considered and compared with the deterministic models
Meet, Discuss and Trust each other: large versus small groups
In this paper we propose a dynamical interpretation of the sociological
distinction between large and small groups of interacting individuals. In the
former case individual behaviors are largely dominated by the group effect,
while in the latter mutual relationships do matter. Numerical and analytical
tools are combined to substantiate our claims.Comment: 12 pages, 4 figure
Emerging structures in social networks guided by opinions’ exchanges
n this paper, we show that the small world and weak ties phenomena can spontaneously emerge in a social network of interacting agents. This dynamics is simulated in the framework of a simplified model of opinion diffusion in an evolving social network where agents are made to interact, possibly update their beliefs and modify the social relationships according to the opinion exchange
Noisy continuous--opinion dynamics
We study the Deffuant et al. model for continuous--opinion dynamics under the
influence of noise. In the original version of this model, individuals meet in
random pairwise encounters after which they compromise or not depending of a
confidence parameter. Free will is introduced in the form of noisy
perturbations: individuals are given the opportunity to change their opinion,
with a given probability, to a randomly selected opinion inside the whole
opinion space. We derive the master equation of this process. One of the main
effects of noise is to induce an order-disorder transition. In the disordered
state the opinion distribution tends to be uniform, while for the ordered state
a set of well defined opinion groups are formed, although with some opinion
spread inside them. Using a linear stability analysis we can derive approximate
conditions for the transition between opinion groups and the disordered state.
The master equation analysis is compared with direct Monte-Carlo simulations.
We find that the master equation and the Monte-Carlo simulations do not always
agree due to finite-size induced fluctuations that we analyze in some detail
Measuring the mixing efficiency in a simple model of stirring:some analytical results and a quantitative study via Frequency Map Analysis
We prove the existence of invariant curves for a --periodic Hamiltonian
system which models a fluid stirring in a cylindrical tank, when is small
and the assigned stirring protocol is piecewise constant. Furthermore, using
the Numerical Analysis of the Fundamental Frequency of Laskar, we investigate
numerically the break down of invariant curves as increases and we give a
quantitative estimate of the efficiency of the mixing.Comment: 10 figure
Birth and Death in a Continuous Opinion Dynamics Model. The consensus case
We here discuss the process of opinion formation in an open community where
agents are made to interact and consequently update their beliefs. New actors
(birth) are assumed to replace individuals that abandon the community (deaths).
This dynamics is simulated in the framework of a simplified model that accounts
for mutual affinity between agents. A rich phenomenology is presented and
discussed with reference to the original (closed group) setting. Numerical
findings are supported by analytical calculations.Comment: 13 pages, 6 figure
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