arXiv subjects
Publications and source records attributed to Timoteo Carletti.
We hereby propose a model of opinion dynamics where individuals update their beliefs because of interactions in acquaintances' group. The model exhibit a non trivial behavior that we discuss as a function of the main involved parameters. Results are reported on the average number of opinion clusters and the time needed to form such clusters.
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.
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.
We study the dynamics of public opinion in a model in which agents change their opinions as a result of random binary encounters if the opinion difference is below their individual thresholds that evolve over time. We ground these thresholds in a simple individual cost-benefit analysis with linear benefits of diversity and quadratic communication costs. We clarify and deepen the results of earlier continuous-opinion dynamics models (Deffuant et al., Adv Complex Systems 2000; Weisbuch et al., Complexity 2002) and establish several new results regarding the patterns of opinions in the asymptotic state and the cluster formation time.
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.
We here propose a model to simulate the process of opinion formation, which accounts for the mutual affinity between interacting agents. Opinion and affinity evolve self-consistently, manifesting a highly non trivial interplay. A continuous transition is found between single and multiple opinion states. Fractal dimension and signature of critical behaviour are also reported. A rich phenomenology is presented and discussed with reference to corresponding psychological implications.
We prove the existence of invariant curves for a $T$--periodic Hamiltonian system which models a fluid stirring in a cylindrical tank, when $T$ 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 $T$ increases and we give a quantitative estimate of the efficiency of the mixing.
The phase--portrait of the second order differential equation: $$\ddot x+\sum_{l=0}^nf_l(x) \dot x^l=0 ,$$ is studied. Some results concerning existence, non--existence and uniqueness of limit cycles are presented. Among these, a generalization of the classical Massera uniqueness result is proved.
In this paper we give sufficient conditions to ensure uniqueness of limit cycles for a class of planar vector fields. We also exhibit a class of examples with exactly one limit cycle.
We study the orbit behavior of a germ of an analytic vector field of $(C^n,0)$, $n \geq 2$. We prove that if its linear part is semisimple, non--resonant and verifies a Bruno--like condition, then the origin is effectively stable: stable for finite but exponentially long times.
We consider the Liénard equation and we give a sufficient condition to ensure existence and uniqueness of limit cycles. We compare our result with some other existing ones and we give some applications.
We study the 1/2--Complex Bruno function and we produce an algorithm to evaluate it numerically, giving a characterization of the monoid $\hat{\mathcal{M}}=\mathcal{M}_T\cup \mathcal{M}_S$. We use this algorithm to test the Marmi--Moussa--Yoccoz Conjecture about the Hölder continuity of the function $z\mapsto -i\mathbf{B}(z)+ \log U(e^{2πi z})$ on $\{z\in \mathbb{C}: \Im z \geq 0 \}$, where $\mathbf{B}$ is the 1/2--complex Bruno function and $U$ is the Yoccoz function. We give a positive answer to an explicit question of S. Marmi et al [MMY2001].
The classical Lagrange inversion formula is extended to analytic and non--analytic inversion problems on non--Archimedean fields. We give some applications to the field of formal Laurent series in $n$ variables, where the non--analytic inversion formula gives explicit formal solutions of general semilinear differential and $q$--difference equations. We will be interested in linearization problems for germs of diffeomorphisms (Siegel center problem) and vector fields. In addition to analytic results, we give sufficient condition for the linearization to belong to some Classes of ultradifferentiable germs, closed under composition and derivation, including Gevrey Classes. We prove that Bruno's condition is sufficient for the linearization to belong to the same Class of the germ, whereas new conditions weaker than Bruno's one are introduced if one allows the linearization to be less regular than the germ. This generalizes to dimension $n> 1$ some results of [CarlettiMarmi]. Our formulation of the Lagrange inversion formula by mean of trees, allows us to point out the strong similarities existing between the two linearization problems, formulated (essentially) with the same functional equation. For analytic vector fields of $\C^2$ we prove a quantitative estimate of a previous qualitative result of [MatteiMoussu] and we compare it with a result of [YoccozPerezMarco].
We study the Siegel--Schröder center problem on the linearization of analytic germs of diffeomorphisms in several complex variables, in the Gevrey--$s$, $s>0$ category. We introduce a new arithmetical condition of Bruno type on the linear part of the given germ, which ensures the existence of a Gevrey--$s$ formal linearization. We use this fact to prove the effective stability, i.e. stability for finite but long time, of neighborhoods of the origin for the analytic germ.