• Title, Summary, Keyword: global stability

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Bypass, homotopy path and local iteration to compute the stability point

  • Fujii, Fumio;Okazawa, Shigenobu
    • Structural Engineering and Mechanics
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    • v.5 no.5
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    • pp.577-586
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    • 1997
  • In nonlinear finite element stability analysis of structures, the foremost necessary procedure is the computation to precisely locate a singular equilibrium point, at which the instability occurs. The present study describes global and local procedures for the computation of stability points including bifurcation points and limit points. The starting point, at which the procedure will be initiated, may be close to or arbitrarily far away from the target point. It may also be an equilibrium point or non-equilibrium point. Apart from the usual equilibrium path, bypass and homotopy path are proposed as the global path to the stability point. A local iterative method is necessary, when it is inspected that the computed path point is sufficiently close to the stability point.

Uniform ultimate boundedness and global asympotic stabilization for systems with mis-matched uncertainties (비 매칭 불확실성이 있는 비선형시스템의 균일 종국적 유계성 및 대역적 점근 안정성)

  • 장충환;성열완;이건일
    • Journal of the Korean Institute of Telematics and Electronics S
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    • v.35S no.7
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    • pp.29-36
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    • 1998
  • In this paper we propose a control law using a Lyapunov-like function that makes stable the systems which have mis-matched uncertainties. The existing control law using a Lyapunov-like function, which gives global saymptotic stability, is designed under the assumption of a targetsystem to be stable locally. But we broaden here the class of target systems by designing the control law which can give uniform ultimate boundedness to even the systems not satisfing the locally asymptotic stability. And we also show that the control law giving global asymptotic stability can be designed more systematically through using the uniform ultimate boundedness.

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GLOBAL EXPONENTIAL STABILITY OF BAM FUZZY CELLULAR NEURAL NETWORKS WITH DISTRIBUTED DELAYS AND IMPULSES

  • Li, Kelin;Zhang, Liping
    • Journal of applied mathematics & informatics
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    • v.29 no.1_2
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    • pp.211-225
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    • 2011
  • In this paper, a class of bi-directional associative memory (BAM) fuzzy cellular neural networks with distributed delays and impulses is formulated and investigated. By employing an integro-differential inequality with impulsive initial conditions and the topological degree theory, some sufficient conditions ensuring the existence and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the delay kernel functions and system parameters. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.

ANALYSIS OF A NONAUTONOMOUS PREDATOR-PREY MODEL INCORPORATING A PREY REFUGE AND TIME DELAY

  • Samanta, G.P.;Garain, D.N.
    • Journal of applied mathematics & informatics
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    • v.29 no.3_4
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    • pp.955-967
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    • 2011
  • In this paper we have considered a nonautonomous predator-prey model with discrete time delay due to gestation, in which there are two prey habitats linked by isotropic migration. One prey habitat contains a predator and the other (a refuge) does not. Here, we have established some sufficient conditions on the permanence of the system by using in-equality analytical technique. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. We have observed that the per capita migration rate among two prey habitats and the time delay has no effect on the permanence of the system but it has an effect on the global asymptotic stability of this model. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

Reliability analyses of a prototype soil nail wall using regression models

  • Sivakumar Babu, G.L.;Singh, Vikas Pratap
    • Geomechanics and Engineering
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    • v.2 no.2
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    • pp.71-88
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    • 2010
  • Soil nailing technique is being widely used for stabilization of vertical cuts because of its economic, environment friendly and speedy construction. Global stability and lateral displacement are the two important stability criteria for the soil nail walls. The primary objective of the present study is to evaluate soil nail wall stability criteria under the influence of in-situ soil variability. Finite element based numerical experiments are performed in accordance with the methodology of $2^3$ factorial design of experiments. Based on the analysis of the observations from numerical experiments, two regression models are developed, and used for reliability analyses of global stability and lateral displacement of the soil nail wall. A 10 m high prototype soil nail wall is considered for better understanding and to highlight the practical implications of the present study. Based on the study, lateral displacements beyond 0.10% of vertical wall height and variability of in-situ soil parameters are found to be critical from the stability criteria considerations of the soil nail wall.

DETERMINATION OF GLOBAL STABILITY OF THE SLOSH MOTION IN A SPACECRAFT VIA NUMERICAL EXPERIMENT (수치적 실험에 의한 위성 내부 유동체의 안정-불안정 영역 판별)

  • 강자영
    • Journal of Astronomy and Space Sciences
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    • v.20 no.4
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    • pp.351-358
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    • 2003
  • The global stability of the attitude motion of a spin-stabilized space vehicle is investigated by performing numerical experiment. In the previous study, a stationary solution and a particular resonant condition for a given model were found by using analytical method but failed to represent the system stability over parameter values near and off the stationary points. Accordingly, as an extension of the previous work, this study performs numerical experiment to investigate the stability of the system across the parameter space and determines stable and unstable regions of the design parameters of the system.

Analysis on Failure Causes and Stability of Reinforced Earth Wall Based on a Field Case (현장사례를 이용한 보강토옹벽의 파괴원인 및 안정성 분석)

  • Hong, Kikwon;Han, Jung-Geun;Lee, Jong-Young;Park, Jai-Seok
    • Journal of the Korean Geosynthetics Society
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    • v.12 no.1
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    • pp.109-114
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    • 2013
  • This paper describes the global stability of the reinforced earth wall, which was collapsed by heavy rainfall. The seepage analysis was conducted to confirm the change effect of groundwater level on slope with reinforced earth wall. The seepage analysis result confirmed that the change of groundwater level is greatly influenced by rainfall. According to the change of groundwater level, the global stability analysis with reinforced earth wall was conducted based on the results of seepage analysis. The safety factor of the slope was 0.476 when the wall is collapsed firstly. The collapse cause analyzed that soil strength was weaken because the ground was saturated by continuous rainfall. Therefore, the global stability, which is considered heavy rainfall, should be conducted at design and construction of reinforced earth wall.

GLOBAL THRESHOLD DYNAMICS IN HUMORAL IMMUNITY VIRAL INFECTION MODELS INCLUDING AN ECLIPSE STAGE OF INFECTED CELLS

  • ELAIW, A.M.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.19 no.2
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    • pp.137-170
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    • 2015
  • In this paper, we propose and analyze three viral infection models with humoral immunity including an eclipse stage of infected cells. The incidence rate of infection is represented by bilinear incidence and saturated incidence in the first and second models, respectively, while it is given by a more general function in the third one. The neutralization rate of viruses is giv0en by bilinear form in the first two models, while it is given by a general function in the third one. For each model, we have derived two threshold parameters, the basic infection reproduction number which determines whether or not a chronic-infection can be established without humoral immunity and the humoral immune response activation number which determines whether or not a chronic-infection can be established with humoral immunity. By constructing suitable Lyapunov functions we have proven the global asymptotic stability of all equilibria of the models. For the third model, we have established a set of conditions on the threshold parameters and on the general functions which are sufficient for the global stability of the equilibria of the model. We have performed some numerical simulations for the third model with specific forms of the incidence and neutralization rates and have shown that the numerical results are consistent with the theoretical results.

GLOBAL COUPLING EFFECTS ON A FREE BOUNDARY PROBLEM FOR THREE-COMPONENT REACTION-DIFFUSION SYSTEM

  • Ham, Yoon-Mee
    • Journal of the Korean Mathematical Society
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    • v.43 no.3
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    • pp.659-676
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    • 2006
  • In this paper, we consider three-component reaction-diffusion system. With an integral condition and a global coupling, this system gives us an interesting free boundary problem. We shall examine the occurrence of a Hopf bifurcation and the stability of solutions as the global coupling constant varies. The main result is that a Hopf bifurcation occurs for global coupling and this motion is transferred to the stable motion for strong global coupling.

Structural system simulation and control via NN based fuzzy model

  • Tsai, Pei-Wei;Hayat, T.;Ahmad, B.;Chen, Cheng-Wu
    • Structural Engineering and Mechanics
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    • v.56 no.3
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    • pp.385-407
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    • 2015
  • This paper deals with the problem of the global stabilization for a class of tension leg platform (TLP) nonlinear control systems. It is well known that, in general, the global asymptotic stability of the TLP subsystems does not imply the global asymptotic stability of the composite closed-loop system. Finding system parameters for stabilizing the control system is also an issue need to be concerned. In this paper, we give additional sufficient conditions for the global stabilization of a TLP nonlinear system. In particular, we consider a class of NN based Takagi-Sugeno (TS) fuzzy TLP systems. Using the so-called parallel distributed compensation (PDC) controller, we prove that this class of systems can be globally asymptotically stable. The proper design of system parameters are found by a swarm intelligence algorithm called Evolved Bat Algorithm (EBA). An illustrative example is given to show the applicability of the main result.