scholarly journals Parameters Estimation and Stability Analysis of Nonlinear Fractional-Order Economic System Based on Empirical Data

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Lei He ◽  
Xiong Wang
Keyword(s):  
Genetic Algorithm ◽  
Stability Analysis ◽  
Dynamical Systems ◽  
Fractional Derivative ◽  
Empirical Data ◽  
Parameters Estimation ◽  
Stability Criteria ◽  
The Us ◽  
Novel Method ◽  
The Stability

This paper is devoted to propose a novel method for studying the macroeconomic system with fractional derivative, which can depict the memory property of actual data of economic variables. First of all, we construct a constrained optimal problem to evaluate the coefficients of nonlinear fractional financial system based on empirical data and design the corresponding genetic algorithm. Then, based on the stability criteria of fractional dynamical systems, the methodology of stability analysis is proposed to investigate the stability of the estimated nonlinear fractional dynamic system. Finally, our method is applied to discuss the macroeconomic system of the US, Australia, and UK to demonstrate its effectiveness and applicability.

A Comparative Study of Liapunov Stability Analyses of Flexible Damped Satellites

1978 ◽  
Vol 45 (3) ◽  
pp. 657-663 ◽  
Author(s):  
H. B. Hablani ◽  
S. K. Shrivastava
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Comparative Study ◽  
Density Function ◽  
Orbital Plane ◽  
Hybrid Dynamical Systems ◽  
Stability Criteria ◽  
Liapunov Stability ◽  
Dynamic Potential ◽  
The Stability

A literal Liapunov stability analysis of a spacecraft with flexible appendages often requires a division of the associated dynamic potential into as many dependent parts as the number of appendages. First part of this paper exposes the stringency in the stability criteria introduced by such a division and shows it to be removable by a “reunion policy.” The policy enjoins the analyst to piece together the sets of criteria for each part. Employing reunion the paper then compares four methods of the Liapunov stability analysis of hybrid dynamical systems illustrated by an inertially coupled, damped, gravity stabilized, elastic spacecraft with four gravity booms having tip masses and a damper rod, all skewed to the orbital plane. The four methods are the method of test density function, assumed modes, and two and one-integral coordinates. Superiority of one-integral coordinate approach is established here. The design plots demonstrate how elastic effects delimit the satellite boom length.

scholarly journals The Stability Criteria with Compound Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yazhuo Zhang ◽  
Baodong Zheng
Keyword(s):  
Dynamical Systems ◽  
Spectral Property ◽  
Discrete Dynamical Systems ◽  
Asymptotical Stability ◽  
Hopf Bifurcations ◽  
Stability Criteria ◽  
Bifurcation Problem ◽  
Compound Matrices ◽  
The Stability ◽  
Schur Stability

The bifurcation problem is one of the most important subjects in dynamical systems. Motivated by M. Li et al. who used compound matrices to judge the stability of matrices and the existence of Hopf bifurcations in continuous dynamical systems, we obtained some effective methods to judge the Schur stability of matrices on the base of the spectral property of compound matrices, which can be used to judge the asymptotical stability and the existence of Hopf bifurcations of discrete dynamical systems.

scholarly journals BUNDLE ADJUSTMENT-BASED STABILITY ANALYSIS METHOD WITH A CASE STUDY OF A DUAL FLUOROSCOPY IMAGING SYSTEM

2018 ◽  
Vol IV-2 ◽  
pp. 9-16 ◽  
Author(s):  
K. Al-Durgham ◽  
D. D. Lichti ◽  
I. Detchev ◽  
G. Kuntze ◽  
J. L. Ronsky
Keyword(s):  
Stability Analysis ◽  
Imaging System ◽  
Parameters Estimation ◽  
System Stability ◽  
Single Camera ◽  
Calibration Data ◽  
Analysis Method ◽  
Advantages And Disadvantages ◽  
Camera Imaging ◽  
The Stability

A fundamental task in photogrammetry is the temporal stability analysis of a camera/imaging-system’s calibration parameters. This is essential to validate the repeatability of the parameters’ estimation, to detect any behavioural changes in the camera/imaging system and to ensure precise photogrammetric products. Many stability analysis methods exist in the photogrammetric literature; each one has different methodological bases, and advantages and disadvantages. This paper presents a simple and rigorous stability analysis method that can be straightforwardly implemented for a single camera or an imaging system with multiple cameras. The basic collinearity model is used to capture differences between two calibration datasets, and to establish the stability analysis methodology. Geometric simulation is used as a tool to derive image and object space scenarios. Experiments were performed on real calibration datasets from a dual fluoroscopy (DF; X-ray-based) imaging system. The calibration data consisted of hundreds of images and thousands of image observations from six temporal points over a two-day period for a precise evaluation of the DF system stability. The stability of the DF system – for a single camera analysis – was found to be within a range of 0.01 to 0.66 mm in terms of 3D coordinates root-mean-square-error (RMSE), and 0.07 to 0.19 mm for dual cameras analysis. It is to the authors’ best knowledge that this work is the first to address the topic of DF stability analysis.

scholarly journals Stability of Fractional Differential Equations with New Generalized Hattaf Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Khalid Hattaf
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Direct Method ◽  
Lyapunov Direct Method ◽  
Science And Engineering ◽  
Fractional Differential ◽  
The Stability

This paper aims to study the stability of fractional differential equations involving the new generalized Hattaf fractional derivative which includes the most types of fractional derivatives with nonsingular kernels. The stability analysis is obtained by means of the Lyapunov direct method. First, some fundamental results and lemmas are established in order to achieve the goal of this study. Furthermore, the results related to exponential and Mittag–Leffler stability existing in recent studies are extended and generalized. Finally, illustrative examples are presented to show the applicability of our main results in some areas of science and engineering.

A New Method for Equilibria and Stability Analysis of Nonlinear Dynamical Systems

2014 ◽  
Vol 534 ◽  
pp. 131-136
Author(s):  
Long Cao ◽  
Yi Hua Cao
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Numerical Continuation ◽  
Vehicle Model ◽  
Nonlinear Dynamical ◽  
Novel Method ◽  
Linearized System ◽  
Continuation Algorithm

A novel method based on numerical continuation algorithm for equilibria and stability analysis of nonlinear dynamical system is introduced and applied to an aircraft vehicle model. Dynamical systems are usually modeled with differential equations, while their equilibria and stability analysis are pure algebraic problems. The newly-proposed method in this paper provides a way to solve the equilibrium equation and the eigenvalues of the locally linearized system simultaneously, which avoids QR iterations and can save much time.

Steady-State and Transient Dynamical Systems Analysis of Uncoupled and Coupled Very Large Amplitude Roll Response of a Vessel in Regular and Random Waves

2006 ◽  
Author(s):  
Jeffrey M. Falzarano ◽  
Srinivas Vishnubhotla ◽  
Sarah E. Juckett
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Dynamical Systems ◽  
Large Amplitude ◽  
Early Stage ◽  
Static Stability ◽  
Random Waves ◽  
The Us ◽  
Us Navy ◽  
Regular And Random Waves

This paper contains the most recent results of our analysis of the DTMB 5415 model hull. This hull is an early stage version of the US Navy’s DDG-51 and approximately represents the last traditional destroyer hull form designed, built and operated by the US Navy. Moreover, the US Navy has recently proposed an alternative simulation based approach to traditional static stability analysis for advanced hull forms. Static stability analysis has been in use by the US Navy for at least 50 years. This paper proposes an alternative analysis technique which uses modern techniques of dynamical systems to analyze the large amplitude (nonlinear) roll response of a vessel in waves. The technique considers the steady state (local) roll response, the transient (global) roll response in both regular and random waves. Moreover, the effects of coupling, damping and reduced GM are all investigated.

Stability of time-dependent rotational Couette flow Part 2. Stability analysis

1971 ◽  
Vol 48 (2) ◽  
pp. 365-384 ◽  
Author(s):  
C. F. Chen ◽  
R. P. Kirchner
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Kinetic Energy ◽  
Initial Value Problem ◽  
Basic Flow ◽  
The Other ◽  
Time Dependent ◽  
Stability Criteria ◽  
Initial Value ◽  
The Stability

The stability of the flow induced by an impulsively started inner cylinder in a Couette flow apparatus is investigated by using a linear stability analysis. Two approaches are taken; one is the treatment as an initial-value problem in which the time evolution of the initially distributed small random perturbations of given wavelength is monitored by numerically integrating the unsteady perturbation equations. The other is the quasi-steady approach, in which the stability of the instantaneous velocity profile of the basic flow is analyzed. With the quasi-steady approach, two stability criteria are investigated; one is the standard zero perturbation growth rate definition of stability, and the other is the momentary stability criterion in which the evolution of the basic flow velocity field is partially taken into account. In the initial-value problem approach, the predicted critical wavelengths agree remarkably well with those found experimentally. The kinetic energy of the perturbations decreases initially, reaches a minimum, then grows exponentially. By comparing with the experimental results, it may be concluded that when the perturbation kinetic energy has grown a thousand-fold, the secondary flow pattern is clearly visible. The time of intrinsic instability (the time at which perturbations first tend to grow) is about ¼ of the time required for a thousandfold increase, when the instability disks are clearly observable. With the quasi-steady approach, the critical times for marginal stability are comparable to those found using the initial-value problem approach. The predicted critical wavelengths, however, are about 1½ to 2 times larger than those observed. Both of these points are in agreement with the findings of Mahler, Schechter & Wissler (1968) treating the stability of a fluid layer with time-dependent density gradients. The zero growth rate and the momentary stability criteria give approximately the same results.

Stability Criteria and Analysis of a Monocolumn Concept

2004 ◽  
Author(s):  
Felipe Cruz Rodrigues de Campos ◽  
Marcos Cueva ◽  
Kazuo Nishimoto ◽  
Ana Paula Dos Santos Costa
Keyword(s):  
Stability Analysis ◽  
Offshore Structures ◽  
Oil Fields ◽  
Stability Criteria ◽  
Offshore Drilling ◽  
Steel Catenary Risers ◽  
Special Concern ◽  
The Stability ◽  
Almost All ◽  
Classification Society

To be classified and approved by a classification society, all offshore structures shall be submitted and analyzed according to standard rules. The stability criteria are based on the IMO–MODU (International Maritime Organization–Mobile Offshore Drilling Units) Code which has reference to almost all types of floating units such as surface, column-stabilized and self elevating, but problems were found when dealing with monocolumn concept due to differences between this concept and those presented by the rules. The monocolumn studied is a floating production system (FPS) platform designed to handle steel catenary risers (SCR) in a depth of 1800 m in Brazilian oil fields. In this project, special concern was given to sea keeping behavior, constructability and security. This paper discusses the last item, focusing on subdivision and stability analysis. In order to overcome difficulties in finding the appropriate criteria, the work was developed using a special criteria, discussed with Det Norske Veritas (DNV) and PETROBRAS, which could be implanted in future classifications for this type of hull.

Search of the Most Dangerous in Slide Slope Stability Analysis Based on Genetic Algorithm

2012 ◽  
Vol 166-169 ◽  
pp. 2535-2538
Author(s):  
Ke Wang ◽  
Chang Ming Wang ◽  
Fang Qi ◽  
Cen Cen Niu
Keyword(s):  
Genetic Algorithm ◽  
Stability Analysis ◽  
Slope Stability ◽  
Slip Surface ◽  
Limit Equilibrium ◽  
Evolutionary Process ◽  
Limit Equilibrium Method ◽  
Slope Stability Analysis ◽  
Equilibrium Method ◽  
The Stability

The traditional limit equilibrium method in the analysis of slope stability not only exists some subjective empirical hypothesis that can not meet the equilibrium of force and moment, but also ignores the effects of internal stress and strain on the slope stability. Furthermore, in the stability of the slope evaluation, limit equilibrium method relies too much on experience when hypothesizing the slope slip surface. So that it makes deviation on slope analysis and stability evaluation. This paper is based on simplified Bishop method used to establish the model of slope stability analysis. And it used genetic algorithms to solve the minimum safety factor and the most dangerous slip surface of slope. It was the arithmetic which simulates organisms genetic evolutionary process and it avoided the traditional methods falling into the local extreme value point easily and error propagation leading to convergence. The algorithm had advantages of higher accuracy, quick convergence and applicability. It showed that the genetic algorithm is accurate and reliable in the analysis of slope stability.

scholarly journals The Stability Analyze of KM. Rejeki Baru Kharisma of Tarakan – Tanjung Selor Route

Teknik ◽  
2021 ◽  
Vol 42 (1) ◽  
pp. 52-62
Author(s):  
Alamsyah Alamsyah ◽  
Zen Zulkarnaen ◽  
Suardi Suardi
Keyword(s):  
Stability Analysis ◽  
Stability Criteria ◽  
Load Case ◽  
Ship Stability ◽  
Intact Stability ◽  
Ship Capsize ◽  
The Stability ◽  
Stability Area ◽  
The Ideal

Ship stability that is not according to the IMO standard will make the ship capsize when operating. The purpose of this research is to determine the cause of the overturn in terms of the stability criteria of the ship. The method used is software  of simulation. Stability analysis is carried out with the load case that occurs in the field when an accident occurs and the ideal loadcase according to PM 104 2017 standards about’s the transportation of operation. The results showed is cargo of goods placed on the roof top (loadcase 1) based on the criteria of Intact Stability; area of the stability arm curve at heeling 0° ~ 30° = 0.9417 m.deg, area 0° ~ 40° = 1,0200 m.deg, 30° ~ 40° = 0.0783 m.deg, GZ value at heeling 30° = 0.029 m, angle of occurrence of maximum GZ = 21.8°, and the initial GMt value = 0.135 m, the results stated that all did not meet the Intact Stability code A.749 criteria, while in it was obtained cargo of goods placed in the hull (loadcase 2) based on Intact Stability; area of the stability arm curve at heeling 0° ~ 30° = 4.5338 m.deg, area 0° ~ 40° = 7.1643 m.deg, area 30° ~ 40° = 2.6305 m.deg, GZ value at heeling 30° = 0.265 m, angle of occurrence of maximum GZ = 34.5°, and the initial GMt value = 0.621 m, the results stated that all met the Intact Stability code A.749 criteria

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