Search results for "Dynamical Systems"
showing 10 items of 476 documents
Hybrid Modelling and Control of a Class of Power Converters With Triangular-Carrier PWM Inputs
2021
In this paper, a new control design procedure for a class of power converters based on hybrid dynamical systems theory is presented. The continuous-time dynamics, as voltage and current signals, and discretetime dynamics, as the on-off state of the switches, are captured with a hybrid model. This model avoids the use of averaged and approximated models and includes the PWM as well as the sample-and-hold mechanism, commonly used in the industry. Then, another simplified hybrid system, whose trajectories match with the original one, is selected to design the controller and to analyse stability properties. Finally, an estimation of the chattering in steady state of the voltage and current sign…
Random attractors for stochastic lattice systems with non-Lipschitz non-linearity
2012
In this paper we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an additive noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems we prove the existence of a random compact global attractor.
Structural Stability
2020
The notion of structural stability was first introduced by the Russian math- ematicians Alexandr Andronov and Lev Pontryagin (cf. Andronov and Potryangin 1937). However, there are traces of such a concept in the work of the French math- ematician Henry Poincaré (cf. Poincaré 1880). In more recent years, interesting developments about structural stability included writings of important math- ematicians like Mauricìo Peixoto (cf. at least Peixoto 1960), Stephen Smale (cf. at least Smale 1971) and René Thom (1972, 1980) (see structural morpho- dynamics). From an intuitive point of view, structural stability refers to a particular systemic property known as robustness. Put in general terms, a s…
Seifert manifolds admitting partially hyperbolic diffeomorphisms
2017
We characterize which 3-dimensional Seifert manifolds admit transitive partially hyperbolic diffeomorphisms. In particular, a circle bundle over a higher-genus surface admits a transitive partially hyperbolic diffeomorphism if and only if it admits an Anosov flow.
Surface homeomorphisms with zero dimensional singular set
1998
We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set is totally disconnected, then f is topologically conjugate to a conformal transformation.
Distributed Consensus on Boolean Information
2009
Abstract In this paper we study the convergence towards consensus on information in a distributed system of agents communicating over a network. The particularity of this study is that the information on which the consensus is seeked is not represented by real numbers, rather by logical values or sets. Whereas the problems of allowing a network of agents to reach a consensus on logical functions of input events, and that of agreeing on set–valued information, have been separately addressed in previous work, in this paper we show that these problems can indeed be attacked in a unified way in the framework of Boolean distributed information systems. Based on a notion of contractivity for Bool…
On the problem of visualizing point distributions in high dimensional spaces
1995
Abstract Exploring dynamical systems with the aid of computer graphics requires that the relevant structures can be seen and be noticed. This poses special problems if the system is multidimensional, and it has to be decided which kind of projection serves the purpose. I propose using the mathematical frame of categories and functors to describe the process of visualization. This allows detecting and analyzing possible sources of misinterpretation in a formal way. The distribution of distances of embedded electroencephalographic data from a fixed reference point is used as an example for discussing some aspects of the visualization process. The multidimensional p-norms are an example of a p…
Dirac physical measures for generic diffeomorphisms
2016
We prove that, for a $C^1$ generic diffeomorphism, the only Dirac physical measures with dense statistical basin are those supported on sinks.
European Option Pricing with Transaction Costs and Stochastic Volatility: an Asymptotic Analysis
2015
In this paper the valuation problem of a European call option in presence of both stochastic volatility and transaction costs is considered. In the limit of small transaction costs and fast mean reversion, an asymptotic expression for the option price is obtained. While the dominant term in the expansion it is shown to be the classical Black and Scholes solution, the correction terms appear at $O(\varepsilon^{1/2})$ and $O(\varepsilon)$. The optimal hedging strategy is then explicitly obtained for the Scott's model.
On the coupling between agent internal and agent/ environmental dynamics: Development of spatial representations in evolving autonomous robots
2008
In this article we describe how a population of evolving robots can autonomously develop forms of spatial representation which allow them to self-localize and to discriminate different locations of their environment by integrating sensory-motor information over time. The evolving robots also display a remarkable ability to generalize their skill in new environmental conditions that they have never experienced before. The analysis of the obtained results indicates that the evolved robots come up with simple and robust solutions that exploit quasi-periodic limit cycle dynamics emerging from the coupling between the robot/environmental dynamics and a robot's internal dynamics. More specifical…