Search results for "Dynamical Systems"
showing 10 items of 476 documents
Optimal control and Clairaut-Liouville metrics with applications
2014
The work of this thesis is about the study of the conjugate and cut loci of 2D riemannian or almost-riemannian metrics. We take the point of view of optimal control to apply the Pontryagin Maximum Principle in the purpose of characterize the extremals of the problem considered.We use geometric, numerical and integrability methods to study some Liouville and Clairaut-Liouville metrics on the sphere. In the degenerate case of revolution, the study of the ellipsoid uses geometric methods to fix the cut locus and the nature of the conjugate locus in the oblate and prolate cases. In the general case, extremals will have two distinct type of comportment which correspond to those observed in the r…
Iterative closure method for non-linear systems driven by polynomials of Gaussian filtered processes
2008
This paper concerns the statistical characterization of the non-Gaussian response of non-linear systems excited by polynomial forms of filtered Gaussian processes. The non-Gaussianity requires the computation of moments of any order. The problem is solved profiting from both the stochastic equivalent linearization (EL), and the moment equation approach of Ito's stochastic differential calculus through a procedure divided into two parts. The first step requires the linearization of the system, while retaining the non-linear excitation; the response statistical moments are calculated exactly, and constitute a first estimate of the moments of the actual non-linear system. In the second step, t…
Asymptotic Behaviour of a Logistic Lattice System
2014
In this paper we study the asymptotic behaviour of solutions of a lattice dynamical system of a logistic type. Namely, we study a system of in nite ordinary di erential equations which can be obtained after the spatial discretization of a logistic equation with di usion. We prove that a global attractor exists in suitable weighted spaces of sequences.
On Differential Equations with Delay in Banach Spaces and Attractors for Retarded Lattice Dynamical Systems
2014
In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation in a Banach space by assuming that the nonlinear term is in some sense weakly continuous. We then apply this result to a lattice dynamical system with delay, proving also the existence of a global compact attractor for such system.
Do crossover functions depend on the shape of the interaction profile?
1999
We examine the crossover from classical to non-classical critical behaviour in two-dimensional systems with a one-component order parameter. Since the degree of universality of the corresponding crossover functions is still subject to debate, we try to induce non-universal effects by adding interactions with a second length scale. Although the crossover functions clearly depend on the range of the interactions, they turn out to be remarkably robust against further variation of the interaction profile. In particular, we find that the earlier observed non-monotonic crossover of the effective susceptibility exponent occurs for several qualitatively different shapes of this profile.
What is a physical measure of spatial inhomogeneity comparable to the mathematical approach?
1999
A linear transformation f(S) of configurational entropy with length scale dependent coefficients as a measure of spatial inhomogeneity is considered. When a final pattern is formed with periodically repeated initial arrangement of point objects the value of the measure is conserved. This property allows for computation of the measure at every length scale. Its remarkable sensitivity to the deviation (per cell) from a possible maximally uniform object distribution for the length scale considered is comparable to behaviour of strictly mathematical measure h introduced by Garncarek et al. in [2]. Computer generated object distributions reveal a correlation between the two measures at a given l…
The minimal model of Hahn for the Calvin cycle.
2018
There are many models of the Calvin cycle of photosynthesis in the literature. When investigating the dynamics of these models one strategy is to look at the simplest possible models in order to get the most detailed insights. We investigate a minimal model of the Calvin cycle introduced by Hahn while he was pursuing this strategy. In a variant of the model not including photorespiration it is shown that there exists exactly one positive steady state and that this steady state is unstable. For generic initial data either all concentrations tend to infinity at lates times or all concentrations tend to zero at late times. In a variant including photorespiration it is shown that for suitable v…
Linear dynamics induced by odometers
2022
Weighted shifts are an important concrete class of operators in linear dynamics. In particular, they are an essential tool in distinguishing variety dynamical properties. Recently, a systematic study of dynamical properties of composition operators on $L^p$ spaces has been initiated. This class of operators includes weighted shifts and also allows flexibility in construction of other concrete examples. In this article, we study one such concrete class of operators, namely composition operators induced by measures on odometers. In particular, we study measures on odometers which induce mixing and transitive linear operators on $L^p$ spaces.
Control of Power Converters with Hybrid Affine Models and Pulse-Width Modulated Inputs
2021
In this paper, hybrid dynamical systems theory is applied to the analysis and control of switched converters with Pulse-Width Modulated (PWM) inputs. The system is described by a state-space model with continuous flows and discrete jumps, without averaged equations. The modulation effects are captured in full without using time-dependent signals, by enlarging the state vector to include the PWM waveform generation process. Furthermore, the sample-and-hold mechanism associated with the sampling frequency is also taken into account with this approach. A control law is proposed based on a Lyapunov function candidate. Furthermore, convergence sets and the steady state jitter, inherent to PWM-ba…
The Lyapunov dimension formula for the global attractor of the Lorenz system
2015
The exact Lyapunov dimension formula for the Lorenz system has been analytically obtained first due to G.A.Leonov in 2002 under certain restrictions on parameters, permitting classical values. He used the construction technique of special Lyapunov-type functions developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters of the system such that all the equilibria of the system are hyperbolically unstable. In the present work it is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values, which include all parameters satisfying the …