Search results for "nonlinear analysis"

Stability of charge-pump phase-locked loops : the hold-in and pull-in ranges

2020

The problem of design and analysis of synchronization control circuits is a challenging task for many applications: satellite navigation, digital communication, wireless networks, and others. In this article the Charge-Pump Phase-Locked Loop (CP-PLL) electronic circuit, which is used for frequency synthesis and clock generation in computer architectures, is studied. Analysis of CP-PLL is not trivial: full mathematical model, rigorous definitions, and analysis still remain open issues in many respects. This article is devoted to development of a mathematical model, taking into account engineering aspects of the circuit, interpretation of core engineering problems, definition in relation to m…

Entropy-Based Detection of Complexity and Nonlinearity in Short-Term Heart Period Variability under different Physiopathological States

2020

We compare different estimators of a popular en-tropy-based nonlinear dynamic measure, i.e. the conditional entropy (CE), as regards their ability to assess the complexity and nonlinearity of short-term heart rate variability (HRV). The CE is computed using binning, kernel and nearest neighbor entropy estimators in HRV time series measured from young, old and post-myocardial infarction patients studied at rest and during orthostatic stress. We find that the three estimators yield similar patterns of CE, but different patterns of nonlinear dynamics, across groups and conditions. These results suggest that the strategy for CE estimation is not crucial for the quantification of complexity, but…

Nonlinear dynamical model of Costas loop and an approach to the analysis of its stability in the large

2015

The analysis of the stability and numerical simulation of Costas loop circuits for highfrequency signals is a challenging task. The problem lies in the fact that it is necessary to simultaneously observe very fast time scale of the input signals and slow time scale of phase difference between the input signals. To overcome this difficult situation it is possible, following the approach presented in the classical works of Gardner and Viterbi, to construct a mathematical model of Costas loop, in which only slow time change of signal's phases and frequencies is considered. Such a construction, in turn, requires the computation of phase detector characteristic, depending on the waveforms of the…

Nonlinear dynamical model of Costas loop and an approach to the analysis of its stability in the large

2015

The analysis of the stability and numerical simulation of Costas loop circuits for high-frequency signals is a challenging task. The problem lies in the fact that it is necessary to simultaneously observe very fast time scale of the input signals and slow time scale of phase difference between the input signals. To overcome this difficult situation it is possible, following the approach presented in the classical works of Gardner and Viterbi, to construct a mathematical model of Costas loop, in which only slow time change of signal?s phases and frequencies is considered. Such a construction, in turn, requires the computation of phase detector characteristic, depending on the waveforms of th…

The Egan problem on the pull-in range of type 2 PLLs

2021

In 1981, famous engineer William F. Egan conjectured that a higher-order type 2 PLL with an infinite hold-in range also has an infinite pull-in range, and supported his conjecture with some third-order PLL implementations. Although it is known that for the second-order type 2 PLLs the hold-in range and the pull-in range are both infinite, the present paper shows that the Egan conjecture may be not valid in general. We provide an implementation of the third-order type 2 PLL, which has an infinite hold-in range and experiences stable oscillations. This implementation and the Egan conjecture naturally pose a problem, which we will call the Egan problem: to determine a class of type 2 PLLs for …

Numerical seismic performance of a rammed earth dwelling considering the use of a textile reinforced mortar system

Rammed earth buildings represent a considerable portion of the existing vernacular building stock of several countries and they are very common in the southern region of Portugal. The historical and architectural values of these constructions, along with their recognized high seismic vulnerability, have made the structural rehabilitation of earthen buildings a priority among the scientific community. Despite some recent studies, the prediction of the seismic response of these buildings is still a challenging task. This paper presents the results of a numerical investigation on the seismic behaviour of a representative rammed earth building located in Alentejo (South of Portugal). Numerical …

Pattern formation driven by cross-diffusion

2009

In this work we are interested in describing the mechanism of pattern formation for a reaction-diffusion system with nonlinear diffusion terms (which take into account the self and the cross-diffusion effects). The reaction terms are chosen of the Lotka-Volterra type in the competitive interaction case. The cross-diffusion is proved to be the key mechanism of pattern formation via a linear stability analysis. A weakly nonlinear multiple scales analysis is carried out to predict the amplitude and the form of the pattern close to the bifurcation threshold. In particular, the Stuart-Landau equation which rules the evolution of the amplitude of the most unstable mode is found. In the subcritica…

Cross-diffusion driven instability for a nonlinear reaction-diffusion system

2008

In this work we investigate the possibility of the pattern formation for a system of two coupled reaction-diffusion equations. The nonlinear diffusion terms has been introduced to describe the tendency of two competing species to diffuse faster (than predicted by the usual linear diffusion) toward lower densities areas. The reaction terms are chosen of the Lotka-Volterra type in the competitive interaction case. The system is supplemented with the initial conditions and no-flux boundary conditions. Through a linear stability analysis we find the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show h…

Harmonic balance analysis of pull-in range and oscillatory behavior of third-order type 2 analog PLLs

2020

The most important design parameters of each phase-locked loop (PLL) are the local and global stability properties, and the pull-in range. To extend the pull-in range, engineers often use type 2 PLLs. However, the engineering design relies on approximations which prevent a full exploitation of the benefits of type 2 PLLs. Using an exact mathematical model and relying on a rigorous mathematical thinking this problem is revisited here and the stability and pull-in properties of the third-order type 2 analog PLLs are determined. Both the local and global stability conditions are derived. As a new idea, the harmonic balance method is used to derive the global stability conditions. That approach…

Computation of lock-in range for classic PLL with lead-lag filter and impulse signals

2016

For a classic PLL with square waveform signals and lead-lag filter for all possible parameters lock-in range is computed and corresponding diagrams are given. peerReviewed