Search results for "dynamical system"
showing 10 items of 523 documents
Quantitative ergodicity for some switched dynamical systems
2012
International audience; We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd × E where E is a finite set. The continuous component evolves according to a smooth vector field that switches at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rates and stability conditions for the vector fields we provide explicit exponential upper bounds for the convergence to equilibrium in terms of Wasserstein distances. As an example, we obtain convergence results for a stochastic version of the Morris-Lecar model of neurobiology.
Riemann-Type Definition of the Improper Integrals
2004
Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane's definition of the Lebesgue integral by imposing a Kurzweil-Henstock's condition on McShane's partitions.
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.
Exact stationary solution for a class of non-linear systems driven by a non-normal delta-correlated process
1995
In this paper the exact stationary solution in terms of probability density function for a restricted class of non-linear systems under both external and parametric non-normal delta-correlated processes is presented. This class has been obtained by imposing a given probability distribution and finding the corresponding dynamical system which satisfies the modified Fokker-Planck equation. The effectiveness of the results has been verified by means of a Monte Carlo simulation.
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…