Search results for "dynamical system"
showing 10 items of 523 documents
Transient dynamics of pulse-driven memristors in the presence of a stable fixed point
2019
Abstract Some memristors are quite interesting from the point of view of dynamical systems. When driven by narrow pulses of alternating polarities, their dynamics has a stable fixed point, which may be useful for future applications. We study the transient dynamics of two types of memristors characterized by a stable fixed point using a time-averaged evolution equation. Time-averaged trajectories of the Biolek window function memristor and resistor-threshold type memristor circuit (an effective memristor) are determined analytically, and the times of relaxation to the stable fixed point are found. Our analytical results are in perfect agreement with the results of numerical simulations.
Gradients of O-information: Low-order descriptors of high-order dependencies
2023
O-information is an information-theoretic metric that captures the overall balance between redundant and synergistic information shared by groups of three or more variables. To complement the global assessment provided by this metric, here we propose the gradients of the O-information as low-order descriptors that can characterise how high-order effects are localised across a system of interest. We illustrate the capabilities of the proposed framework by revealing the role of specific spins in Ising models with frustration, and on practical data analysis on US macroeconomic data. Our theoretical and empirical analyses demonstrate the potential of these gradients to highlight the contributio…
A Survey on Dynamic Analysis of the Costas Loop
2015
This survey is devoted to the dynamic analysis of the Costas loop. In particular the acquisition process is analyzed in great detail. Acquision is most conventiently described by a number of frequency and time parameters such as lock-in range, lock-in time, pull-in range, pull-in time, and hold-in range. While for the classical PLL equations for all these parameters have been derived (many of them are approximations, some even crude approximations), this has not yet been carried out for the Costas loop. It is the aim of this analysis to close this gap. The paper starts with an overview on mathematical and physical models (exact and simplified) of the different variants of the Costas loop, c…
Hidden attractors in aircraft control systems with saturated inputs
2017
In the paper, the control problem with limitations on the magnitude and rate of the control action in aircraft control systems, is studied. Existence of hidden oscillations in the case of actuator position and rate limitations is demonstrated by the examples of piloted aircraft pilot involved oscillations (PIO) phenomenon and the airfoil flutter suppression system.
Fixed points of diffeomorphisms, singularities of vector fields and epsilon-neighborhoods of their orbits, the thesis
2013
The thesis deals with recognizing diffeomorphisms from fractal properties of discrete orbits, generated by iterations of such diffeomorphisms. The notion of fractal properties of a set refers to the box dimension, the Minkowski content and their appropriate generalizations, or, in wider sense, to the epsilon-neighborhoods of sets, for small, positive values of parameter epsilon. In the first part of the thesis, we consider the relation between the multiplicity of the fixed point of a real-line diffeomorphism, and the asymptotic behavior of the length of the epsilon-neighborhoods of its orbits. We establish the bijective correspondence. At the fixed point, the diffeomorphisms may be differen…
Lock-in range of classical PLL with impulse signals and proportionally-integrating filter
2016
In the present work the model of PLL with impulse signals and active PI filter in the signal's phase space is described. For the considered PLL the lock-in range is computed analytically and obtained result are compared with numerical simulations.
Integrability and non integrability of some n body problems
2015
We prove the non integrability of the colinear $3$ and $4$ body problem, for any masses positive masses. To deal with resistant cases, we present strong integrability criterions for $3$ dimensional homogeneous potentials of degree $-1$, and prove that such cases cannot appear in the $4$ body problem. Following the same strategy, we present a simple proof of non integrability for the planar $n$ body problem. Eventually, we present some integrable cases of the $n$ body problem restricted to some invariant vector spaces.
Quantifying non-periodicity of non-stationary time series through wavelets
2019
In this paper, we introduce a new wavelet tool for studying the degree of non-periodicity of time series that is based on some recently defined tools, such as the \textit{windowed scalogram} and the \textit{scale index}. It is especially appropriate for non-stationary time series whose characteristics change over time and so, it can be applied to a wide variety of disciplines. In addition, we revise the concept of the scale index and pose a theoretical problem: it is known that if the scale index of a function is not zero then it is non-periodic, but if the scale index of a function is zero, then it is not proved that it has to be periodic. This problem is solved for the particular case of …
Lock-in range of PLL-based circuits with proportionally-integrating filter and sinusoidal phase detector characteristic
2016
In the present work PLL-based circuits with sinusoidal phase detector characteristic and active proportionally-integrating (PI) filter are considered. The notion of lock-in range -- an important characteristic of PLL-based circuits, which corresponds to the synchronization without cycle slipping, is studied. For the lock-in range a rigorous mathematical definition is discussed. Numerical and analytical estimates for the lock-in range are obtained.
Aperiodic chain recurrence classes of $C^1$-generic diffeomorphisms
2022
We consider the space of $C^1$-diffeomorphims equipped with the $C^1$-topology on a three dimensional closed manifold. It is known that there are open sets in which $C^1$-generic diffeomorphisms display uncountably many chain recurrences classes, while only countably many of them may contain periodic orbits. The classes without periodic orbits, called aperiodic classes, are the main subject of this paper. The aim of the paper is to show that aperiodic classes of $C^1$-generic diffeomorphisms can exhibit a variety of topological properties. More specifically, there are $C^1$-generic diffeomorphisms with (1) minimal expansive aperiodic classes, (2) minimal but non-uniquely ergodic aperiodic c…