• Title/Summary/Keyword: Global asymptotic stability

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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.

DYNAMICS OF A CLASS OF NON-AUTONOMOUS SYSTEMS OF TWO NON-INTERACTING PREYS WITH COMMON PREDATOR

  • ELABBASY E. M.;SAKER S. H.
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.195-215
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    • 2005
  • In this paper, we investigate the dynamics of the mathematical model of two non-interacting preys in presence of their common natural enemy (predator) based on the non-autonomous differential equations. We establish sufficient conditions for the permanence, extinction and global stability in the general non-autonomous case. In the periodic case, by means of the continuation theorem in coincidence degree theory, we establish a set of sufficient conditions for the existence of a positive periodic solutions with strictly positive components. Also, we give some sufficient conditions for the global asymptotic stability of the positive periodic solution.

THE DYNAMICS OF POSITIVE SOLUTIONS OF A HIGHER ORDER FRACTIONAL DIFFERENCE EQUATION WITH ARBITRARY POWERS

  • GUMUS, MEHMET;SOYKAN, YUKSEL
    • Journal of applied mathematics & informatics
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    • v.35 no.3_4
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    • pp.267-276
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    • 2017
  • The purpose of this paper is to investigate the local asymptotic stability of equilibria, the periodic nature of solutions, the existence of unbounded solutions and the global behavior of solutions of the fractional difference equation $$x_{n+1}=\frac{^{{\alpha}x}n-1(k+1)}{{\beta}+{\gamma}x^p_{n-k}x^q_{n-(k+2)}}$$, $$n=0,1,{\dots}$$ where the parameters ${\alpha}$, ${\beta}$, ${\gamma}$, p, q are non-negative numbers and the initial values $x_{-(k+2)}$,$x_{-(k+1)}$, ${\dots}$, $x_{-1}$, $x_0{\in}\mathb{R}^+$.

Adaptive Control of Flexible-Link Robots (유연마디 로봇의 적응제어)

  • Lee, Ho-Hun;Kim, Hyeon-Gi
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.7 s.178
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    • pp.1689-1696
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    • 2000
  • This paper proposes a new adaptive control scheme for flexible-link robots. A model-based nonlinear control scheme is designed based on a V-shape Lyapunov function, and then the nonlinear control i s extended to a model-based adaptive control to cope with parametric uncertainties in the dynamic model. The proposed control guarantees the global exponential or global asymptotic stability of the overall control system with all internal signals bounded. The effectiveness of the proposed control is shown by computer simulation.

Delay-dependent Stability Criteria for Uncertain Stochastic Neural Networks with Interval Time-varying Delays (구간 시변 지연이 존재하는 불확실 확률적 뉴럴 네트웍의 지연의존 안전성 판별법)

  • Kwon, Oh-Min;Park, Ju-Hyun;Lee, Sang-Moon
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.57 no.11
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    • pp.2066-2073
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    • 2008
  • In this paper, the problem of global asymptotic stability of uncertain stochastic neural networks with delay is considered. The delay is assumed to be time-varying and belong to a given interval. Based on the Lyapunov stability theory, new delay-dependent stability criteria for the system is derived in terms of LMI(linear matrix inequality). Three numerical examples are given to show the effectiveness of proposed method.

Fuzzy Modeling Technique of Nonlinear Dynamical System and Its Stability Analysis (비선형 시스템의 퍼지 모델링 기법과 안정도 해석)

  • So, Myeong Ok;Ryu, Gil Su;Lee, Jun Tak
    • Journal of Advanced Marine Engineering and Technology
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    • v.20 no.2
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    • pp.101-101
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    • 1996
  • This paper presents the linearized fuzzy modeling technique of nonlinear dynamical system and the stability analysis of fuzzy control system. Firstly, the nonlinear system is partitionized by multiple linear fuzzy subcontrol systems based on fuzzy linguistic variables and fuzzy rules. Secondly, the disturbance adaptaion controllers which guarantee the global asymptotic stability of each fuzzy subsystem by an optimal feedback control law are designed and the stability analysis procedures of the total fuzzy control system using Lyapunov functions and eigenvalues are discussed in detail through a given illustrative example.

Fuzzy Modeling Technique of Nonlinear Dynamic System and Its Stability Analysis (비선형 시스템의 퍼지 모델링 기법과 안정도 해석)

  • 소명옥;류길수;이준탁
    • Journal of Advanced Marine Engineering and Technology
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    • v.20 no.2
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    • pp.33-39
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    • 1996
  • This paper presents the linearized fuzzy modeling technique of nonlinear dynamical system and the stability analysis of fuzzy control system. Firstly, the nonlinear system is partitionized by multiple linear fuzzy subcontrol systems based on fuzzy linguistic variables and fuzzy rules. Secondly, the disturbance adaptaion controllers which guarantee the global asymptotic stability of each fuzzy subsystem by an optimal feedback control law are designed and the stability analysis procedures of the total fuzzy control system using Lyapunov functions and eigenvalues are discussed in detail through a given illustrative example.

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Fuzzy Modeling Technique of Nonlinear Dynamical System and Its Stability Analysis (비선형(非線型) 시스템의 퍼지 모델링 기법과 안정도(安定度) 해석(解析)에 관한 연구)

  • Lee, J.T.;So, M.O.;Lee, S.S.;Ji, S.J.;Kim, T.W.
    • Proceedings of the KIEE Conference
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    • 1995.07b
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    • pp.801-803
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    • 1995
  • This paper presents the linearized fuzzy modeling technique of nonlinear dynamical system and the stability analysis of fuzzy control system. Firstly, the nonlinear system is partitionized by multiple linear fuzzy subcontrol systems based on fuzzy linguistic variables and fuzzy rules. Secondly, the disturbance adaptation controllers which guarrantee the global asymptotic stability of each fuzzy subsystem by an optimal feedback control law are designed and the stability analysis procedures of the total fuzzy control system using Lyapunov functions and eigenvalues are discussed in detail through a given illustrative example.

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Onset of Buoyancy-Driven Convection in a Fluid-Saturated Porous Layer Bounded by Semi-infinite Coaxial Cylinders

  • Kim, Min Chan
    • Korean Chemical Engineering Research
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    • v.57 no.5
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    • pp.723-729
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    • 2019
  • A theoretical analysis was conducted of convective instability driven by buoyancy forces under transient temperature fields in an annular porous medium bounded by coaxial vertical cylinders. Darcy's law and Boussinesq approximation are used to explain the characteristics of fluid motion and linear stability theory is employed to predict the onset of buoyancy-driven motion. The linear stability equations are derived in a global domain, and then cast into in a self-similar domain. Using a spectral expansion method, the stability equations are reformed as a system of ordinary differential equations and solved analytically and numerically. The critical Darcy-Rayleigh number is founded as a function of the radius ratio. Also, the onset time and corresponding wavelength are obtained for the various cases. The critical time becomes smaller with increasing the Darcy-Rayleigh number and follows the asymptotic relation derived in the infinite horizontal porous layer.

Graph Connectivity-free Consensus Algorithm for State-coupled Linear Multi-agent Systems: Adaptive Approach (적응 제어를 이용하여 그래프 연결성을 배제시킨 선형 다개체 시스템의 상태변수 일치 알고리듬)

  • Kim, Ji-Su;Kim, Hong-Keun;Shim, Hyung-Bo;Back, Ju-Hoon
    • Journal of Institute of Control, Robotics and Systems
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    • v.18 no.7
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    • pp.617-621
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    • 2012
  • This paper studies asymptotic consensus problem for linear multi-agent systems. We propose a distributed state feedback control algorithm for solving the problem under fixed and undirected network communication. In contrast with the conventional algorithms that use global information (e.g., graph connectivity), the proposed algorithm only uses local information from neighbors. The principle for achieving asymptotic consensus is that, for each agent, a distributed update law gradually increases the coupling gain of LQR-type feedback and thus, the overall stability of the multi-agent system is recovered by the gain margin of LQR.