Search results for "Systems Theory"
showing 10 items of 220 documents
Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities
2012
AbstractIn this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a multiplicative 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.
Massive evaluation and analysis of Poincar�� recurrences on grids of initial data: a tool to map chaotic diffusion
2020
We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar\'e recurrence statistics on massive grids of initial data or values of parameters. We concentrate on Hamiltonian systems, featuring the method separately for the cases of bounded and non-bounded phase spaces. The embodiments of the method in each of the cases are specific. We compare the performances of the proposed Poincar\'e recurrence method (PRM) and the custom Lyapunov exponent (LE) methods and show that they expose the global dynamics almost identically. However, a major advantage of the new method over the known g…
Stochastic response determination of structural systems modeled via dependent coordinates: a frequency domain treatment based on generalized modal an…
2019
Generalized independent coordinates are typically utilized within an analytical dynamics framework to model the motion of structural and mechanical engineering systems. Nevertheless, for complex systems, such as multi-body structures, an explicit formulation of the equations of motion by utilizing generalized, independent, coordinates can be a daunting task. In this regard, employing a set of redundant coordinates can facilitate the formulation of the governing dynamics equations. In this setting, however, standard response analysis techniques cannot be applied in a straightforward manner. For instance, defining and determining a transfer function within a frequency domain response analysis…
Information Decomposition: A Tool to Dissect Cardiovascular and Cardiorespiratory Complexity
2017
This chapter reports some recent developments of information-theoretic concepts applied to the description of coupled dynamical systems, which allow to decompose the entropy of an assigned target system into components reflecting the information stored in the system and the information transferred to it from the other systems, as well as the nature (synergistic or redundant) of the information transferred to the target. The decomposition leads to well-defined measures of information dynamics which in the chapter will be defined theoretically, computed in simulations of linear Gaussian systems and implemented in practice through the application to heart period, arterial pressure and respirat…
On the classification of dynamical data streams using novel “Anti-Bayesian” techniques
2018
Abstract The classification of dynamical data streams is among the most complex problems encountered in classification. This is, firstly, because the distribution of the data streams is non-stationary, and it changes without any prior “warning”. Secondly, the manner in which it changes is also unknown. Thirdly, and more interestingly, the model operates with the assumption that the correct classes of previously-classified patterns become available at a juncture after their appearance. This paper pioneers the use of unreported novel schemes that can classify such dynamical data streams by invoking the recently-introduced “Anti-Bayesian” (AB) techniques. Contrary to the Bayesian paradigm, tha…
A wavelet-based tool for studying non-periodicity
2010
This paper presents a new numerical approach to the study of non-periodicity in signals, which can complement the maximal Lyapunov exponent method for determining chaos transitions of a given dynamical system. The proposed technique is based on the continuous wavelet transform and the wavelet multiresolution analysis. A new parameter, the \textit{scale index}, is introduced and interpreted as a measure of the degree of the signal's non-periodicity. This methodology is successfully applied to three classical dynamical systems: the Bonhoeffer-van der Pol oscillator, the logistic map, and the Henon map.
Nonlinear System Response for Impulsive Parametric Input
1997
In engineering applications when the intensity of external forces depends on the response of the system, the input is called parametric. In this paper dynamical systems subjected to a parametric deterministic impulse are dealt with. Particular attention has been devoted to the evaluation of the discontinuity of the response when the parametric impulse occurs. The usual forward difference and trapezoidal integration schemes have been shown to provide only approximated solutions of the jump of the response; hence, the exact solution has been pursued and presented under the form of a numerical series. The impulse is represented throughout the paper by means of a classical Dirac’s delta functio…
Short chaotic strings and their behaviour in the scaling region
2008
Coupled map lattices are a paradigm of higher-dimensional dynamical systems exhibiting spatio-temporal chaos. A special case of non-hyperbolic maps are one-dimensional map lattices of coupled Chebyshev maps with periodic boundary conditions, called chaotic strings. In this short note we show that the fine structure of the self energy of this chaotic string in the scaling region (i.e. for very small coupling) is retained if we reduce the length of the string to three lattice points.
Overload breakdown in models for photosynthesis
2015
In many models of the Calvin cycle of photosynthesis it is observed that there are solutions where concentrations of key substances belonging to the cycle tend to zero at late times, a phenomenon known as overload breakdown. In this paper we prove theorems about the existence and non-existence of solutions of this type and obtain information on which concentrations tend to zero when overload breakdown occurs. As a starting point we take a model of Pettersson and Ryde-Pettersson which seems to be prone to overload breakdown and a modification of it due to Poolman which was intended to avoid this effect.
Analytical properties of horizontal visibility graphs in the Feigenbaum scenario
2012
Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [1] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree di…