scholarly journals NEW SUFFICIENT CONDITIONS IN THE GENERALIZED SPECTRUM APPROACH TO DEAL WITH SPECTRAL POLLUTION

2018 ◽  
pp. 595-604
Author(s):  
Ammar Khellaf
Keyword(s):  
Theoretical Foundation ◽  
Sufficient Conditions ◽  
Numerical Results ◽  
Spectral Approach ◽  
Spectrum Method ◽  
Generalized Spectrum ◽  
Spectral Pollution

In this work, we propose new sufficient conditions to solve the spectralpollution problem by using the generalized spectrum method. We give the theoretical foundation of the generalized spectral approach, as well as illustrate its effectivenessby numerical results.

scholarly journals A class of strongly stable approximation for unbounded operators

2019 ◽  
pp. 218-234
Author(s):  
Ammar Khellaf ◽  
Sarra Benarab ◽  
Hamza Guebbai ◽  
Wassim Merchela
Keyword(s):  
Sufficient Conditions ◽  
Theoretical Background ◽  
Spectral Approximation ◽  
Unbounded Operators ◽  
Numerical Application ◽  
Spectrum Method ◽  
Pollution Problem ◽  
Generalized Spectrum ◽  
Spectral Pollution ◽  
Discretization Process

We derive new sufficient conditions to solve the spectral pollution problem by using the generalized spectrum method. This problem arises in the spectral approximation when the approximate matrix may possess eigenvalues which are unrelated to any spectral properties of the original unbounded operator. We develop the theoretical background of the generalized spectrum method as well as illustrate its effectiveness with the spectral pollution. As a numerical application, we will treat the Schr¨odinger’s operator where the discretization process based upon the Kantorovich’s projection.

RESONANT LAYERS IN A PARAMETRICALLY EXCITED PENDULUM

2002 ◽  
Vol 12 (02) ◽  
pp. 409-419 ◽  
Author(s):  
ALBERT C. J. LUO
Keyword(s):  
Hamiltonian Systems ◽  
Analytical Method ◽  
Numerical Approach ◽  
Mapping Method ◽  
Numerical Results ◽  
Numerical Prediction ◽  
Parametrically Excited ◽  
Spectrum Method ◽  
Poincare Mapping ◽  
Energy Increment

The energy increment spectrum method is developed for the numerical prediction of a specific primary resonant layer, and the width of the resonant layer can be estimated through the energy increment spectrum. This numerical approach is applied to investigate the (2M:1)-librational and (M:1)-rotational, resonant layers in a parametrically excited pendulum, and the corresponding analytical conditions for such resonant layers are developed. The numerical approach predicts the appearance and disappearance of resonant layers in nonlinear Hamiltonian systems rather than the conventional Poincaré mapping method. Illustrations of the analytical and numerical results for the appearance and disappearance of the resonant layers are given. The width of the resonant layers in the paremetric pendulum is computed. The analytical method should be further improved through renormalization.

scholarly journals Robust stability of linear perturbed discrete systems with multiple time-delay

2006 ◽  
Vol 60 (3-4) ◽  
pp. 82-86
Author(s):  
Sreten Stojanovic ◽  
Dragutin Debeljkovic ◽  
Ilija Mladenovic
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Discrete Systems ◽  
Numerical Results ◽  
Delay Systems ◽  
Multiple Delays ◽  
Multiple Time ◽  
Time Delay Systems

The paper presents some new sufficient conditions, independent of delay, for the asymptotic stability of a particular class of linear perturbed time-delay systems with multiple delays. The proposed criteria introduce a smaller number of assumptions and are expressed in more natural and simpler mathematical forms. Numerical results are presented to support and illustrate the derived results.

Chaotic Motions in Resonant Separatrix Bands of a Parametrically Excited Pendulum

2000 ◽  
Author(s):  
Albert C. J. Luo
Keyword(s):  
Numerical Results ◽  
Numerical Prediction ◽  
Chaotic Motions ◽  
Parametrically Excited ◽  
Spectrum Method ◽  
Energy Increment

Abstract The analytical conditions for the presence of primary (2M:1)-librational and (M:1)-rotational, resonant bands in a parametrically excited pendulum are obtained. The energy increment spectrum method is also developed for the numerical prediction of a specific primary resonant band. Illustrations of the analytical and numerical results for the appearance and destruction of the resonant bands are given for a comparison.

scholarly journals Dynamic Analysis of a Heterogeneous Diffusive Prey-Predator System in Time-Periodic Environment

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Chuanjun Dai ◽  
He Liu ◽  
Zhan Jin ◽  
Qing Guo ◽  
Yi Wang ◽  
...  
Keyword(s):  
Periodic Solution ◽  
Dynamic Analysis ◽  
Spatial Heterogeneity ◽  
Sufficient Conditions ◽  
Numerical Results ◽  
Analytical Analysis ◽  
Periodic Environment ◽  
Time Periodic ◽  
Predator System

In this paper, a heterogeneous diffusive prey-predator system is first proposed and then studied analytically and numerically. Some sufficient conditions are derived, including permanence and extinction of system and the boundedness of the solution. The existence of periodic solution and its stability are discussed as well. Furthermore, numerical results indicate that both the spatial heterogeneity and the time-periodic environment can influence the permanence and extinction of the system directly. Our numerical results are consistent with the analytical analysis.

Snake-Like Locomotions of Multilink Mechanisms

2003 ◽  
Vol 9 (1-2) ◽  
pp. 235-256 ◽  
Author(s):  
F. L. Chernousko
Keyword(s):  
Dry Friction ◽  
Horizontal Plane ◽  
Sufficient Conditions ◽  
Numerical Results ◽  
Mechanical Parameters ◽  
Average Speed ◽  
Optimal Values ◽  
Rotational Motions

Snake-like locomotions of a three-member linkage equipped with actuators are modeled and investigated. Longitudinal, lateral, and rotational motions of the mechanism along a horizontal plane in the presence of the dry friction are analyzed. The desired motions are presented as a combination of more simple elementary motions. Sufficient conditions are deduced under which these motions are possible. The dependence of the average speed of motions on various geometrical and mechanical parameters is investigated. The optimal values of the parameters which maximize the speed are obtained. The numerical results are presented and discussed.

Analyzing synchronization of time-delayed complex dynamical networks with periodic on-off coupling

2017 ◽  
Vol 31 (28) ◽  
pp. 1750210
Author(s):  
Wang Li ◽  
Yongzheng Sun ◽  
Youquan Liu ◽  
Donghua Zhao
Keyword(s):  
Time Delay ◽  
Coupling Strength ◽  
Sufficient Conditions ◽  
Numerical Results ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Outer Synchronization ◽  
Synchronization Time ◽  
Integer Multiple ◽  
Delay Step

We investigate the synchronization of time-delayed complex dynamical networks with periodic on-off coupling. We derive sufficient conditions for the complete and generalized outer synchronization. Both our analytical and numerical results show that two time-delayed networks can achieve outer synchronization even if the couplings between the two networks switch off periodically. This synchronization behavior is largely dependent of the coupling strength, the on-off period, the on-off rate and the time delay. In particular, we find that the synchronization time nonmonotonically increases as the time delay increases when the time delay step is not equal to an integer multiple of the on-off period.

scholarly journals The Dynamics of a Stochastic SEITRmodel for Tuberculosis with Incomplete Treatment

2021 ◽  
Author(s):  
Xiaodong Wang ◽  
Chunxia Wang ◽  
k wang
Keyword(s):  
Numerical Simulations ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Numerical Results ◽  
Transmission Dynamics ◽  
Environmental Perturbations ◽  
Analytical Results

Abstract In this paper, a stochastic SEITR model is formulated to describe the transmission dynamics of tuberculosis with incompletely treated. Sufficient conditions for the existence of a stationary distribution and extinction are obtained. In addition, numerical simulations are given to illustrate these analytical results. Theoretical and numerical results show that large environmental perturbations can inhibit the spread of tuberculosis.

Eigenvalues computation by the generalized spectrum method of Schrödinger’s operator

2018 ◽  
Vol 37 (5) ◽  
pp. 5965-5980 ◽  
Author(s):  
Ammar Khellaf ◽  
Hamza Guebbai ◽  
Samir Lemita ◽  
Mohamed Zine Aissaoui
Keyword(s):  
Spectrum Method ◽  
Generalized Spectrum

scholarly journals An effective fixpoint semantics for linear logic programs

2001 ◽  
Vol 2 (1) ◽  
pp. 85-122 ◽  
Author(s):  
MARCO BOZZANO ◽  
GIORGIO DELZANNO ◽  
MAURIZIO MARTELLI
Keyword(s):  
Logic Programming ◽  
Petri Nets ◽  
Abstract Interpretation ◽  
Theoretical Foundation ◽  
Linear Logic ◽  
Sufficient Conditions ◽  
Logic Programs ◽  
Bottom Up ◽  
Interesting Class ◽  
Fixpoint Semantics

In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog (Andreoli, 1992) that consists of the language LO (Andreoli & Pareschi, 1991) enriched with the constant 1. We use constraints to symbolically and finitely represent possibly infinite collections of provable goals. We define a fixpoint semantics based on a new operator in the style of TP working over constraints. An application of the fixpoint operator can be computed algorithmically. As sufficient conditions for termination, we show that the fixpoint computation is guaranteed to converge for propositional LO. To our knowledge, this is the first attempt to define an effective fixpoint semantics for linear logic programs. As an application of our framework, we also present a formal investigation of the relations between LO and Disjunctive Logic Programming (Minker et al., 1991). Using an approach based on abstract interpretation, we show that DLP fixpoint semantics can be viewed as an abstraction of our semantics for LO. We prove that the resulting abstraction is correct and complete (Cousot & Cousot, 1977; Giacobazzi & Ranzato, 1997) for an interesting class of LO programs encoding Petri Nets.

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