• Title, Summary, Keyword: global stability

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ON THE ORBITAL STABILITY OF INHOMOGENEOUS NONLINEAR SCHRÖDINGER EQUATIONS WITH SINGULAR POTENTIAL

  • Cho, Yonggeun;Lee, Misung
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.6
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    • pp.1601-1615
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    • 2019
  • We show the existence of ground state and orbital stability of standing waves of nonlinear $Schr{\ddot{o}}dinger$ equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in $H^1$. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in [5, 12] slightly in 3 dimensions.

MEAN SQUARE STABILITY IN A MODIFIED LESLIE-GOWER AND HOLLING-TYPE II PREDATOR-PREY MODEL

  • Pal, Pallav Jyoti;Sarwardi, Sahabuddin;Saha, Tapan;Mandal, Prashanta Kumar
    • Journal of applied mathematics & informatics
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    • v.29 no.3_4
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    • pp.781-802
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    • 2011
  • Of concern in the paper is a Holling-Tanner predator-prey model with modified version of the Leslie-Gower functional response. Dynamical behaviours such as stability, permanence and Hopf bifurcation have been carried out deterministically. Using the normal form theory and center manifold theorem, the explicit formulae determining the stability and direction of Hopf bifurcation have been derived. The deterministic model is extended to a stochastic one by perturbing the growth equation of prey and predator by white and colored noises and finally the mean square stability of the stochastic model systems is investigated analytically. An extensive quantitative analysis has been performed based on numerical computation so as to validate the applicability of the proposed mathematical model.

A new swarm intelligent optimization algorithm: Pigeon Colony Algorithm (PCA)

  • Yi, Ting-Hua;Wen, Kai-Fang;Li, Hong-Nan
    • Smart Structures and Systems
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    • v.18 no.3
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    • pp.425-448
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    • 2016
  • In this paper, a new Pigeon Colony Algorithm (PCA) based on the features of a pigeon colony flying is proposed for solving global numerical optimization problems. The algorithm mainly consists of the take-off process, flying process and homing process, in which the take-off process is employed to homogenize the initial values and look for the direction of the optimal solution; the flying process is designed to search for the local and global optimum and improve the global worst solution; and the homing process aims to avoid having the algorithm fall into a local optimum. The impact of parameters on the PCA solution quality is investigated in detail. There are low-dimensional functions, high-dimensional functions and systems of nonlinear equations that are used to test the global optimization ability of the PCA. Finally, comparative experiments between the PCA, standard genetic algorithm and particle swarm optimization were performed. The results showed that PCA has the best global convergence, smallest cycle indexes, and strongest stability when solving high-dimensional, multi-peak and complicated problems.

Research on Robust Stability Analysis and Worst Case Identification Methods for Parameters Uncertain Missiles

  • Hou, Zhenqian;Liang, Xiaogeng;Wang, Wenzheng
    • International Journal of Aeronautical and Space Sciences
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    • v.15 no.1
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    • pp.63-73
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    • 2014
  • For robust stability analysis of parameters uncertainty missiles, the traditional frequency domain method can only analyze each respective channel at several interval points within uncertain parameter space. Discontinuous calculation and couplings between channels will lead to inaccurate analysis results. A method based on the ${\nu}$-gap metric is proposed, which is able to comprehensively evaluate the robust stability of missiles with uncertain parameters; and then a genetic-simulated annealing hybrid optimization algorithm, which has global and local searching ability, is used to search for a parameters combination that leads to the worst stability within the space of uncertain parameters. Finally, the proposed method is used to analyze the robust stability of a re-entry missile with uncertain parameters; the results verify the feasibility and accuracy of the method.

Clinical presentation and specific stabilizing exercise management in Lumbar segmental instability (요추분절의 불안정성에 대한 임상적 소개와 안정성 운동관리)

  • Jung Yeon-Woo;Bae Sung-Soo
    • The Journal of Korean Physical Therapy
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    • v.15 no.1
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    • pp.155-170
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    • 2003
  • Lumbar segmental instability is considered to represent a significant sub-group within the chronic low back pain population. This condition has a unique clinical presentation that displays its symptoms and movement dysfunction within the neutral zone of the motion segment. The loosening of the motion segment secondary to injury and associated dysfunction of the local muscle system renders it biomechanically vulnerable in the neutral zone. There in evidence of muscle dysfunction related to the control of the movement system. There is a clear link between reduced proprioceptive input, altered slow motor unit recruitment and the development of chronic pain states. Dysfunction in the global and local muscle systems in presented to support the development of a system of classification of muscle function and development of dysfunction related to musculoskeletal pain. The global muscles control range of movement and alignment, and evidence of dysfunction is presented in terms of imbalance in recruitment and length between the global stability muscles and the global mobility muscles. The local stability muscles demonstrate evidence of failure of aeequate segmental control in terms of allowing excessive uncontrolled translation or specific loss of cross-sectional area at the site of pathology Motor recruitment deficits present as altered timing and patterns of recruitment. The evidence of local and global dysfunction allows the development of an integrated model of movement dysfunction. The clinical diagnosis of this chronic low back pain condition is based on the report of pain and the observation of movement dysfunction within the neutral zone and the associated finding of excessive intervertebral motion at the symptomatic level. Four different clinical patterns are described based on the directional nature of the injury and the manifestation of the patient's symptoms and motor dysfunction. A specific stabilizing exercise intervention based on a motor learning model in proposed and evidence for the efficacy of the approach provided.

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Composite adaptive neural network controller for nonlinear systems (비선형 시스템제어를 위한 복합적응 신경회로망)

  • 김효규;오세영;김성권
    • 제어로봇시스템학회:학술대회논문집
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    • pp.14-19
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    • 1993
  • In this paper, we proposed an indirect learning and direct adaptive control schemes using neural networks, i.e., composite adaptive neural control, for a class of continuous nonlinear systems. With the indirect learning method, the neural network learns the nonlinear basis of the system inverse dynamics by a modified backpropagation learning rule. The basis spans the local vector space of inverse dynamics with the direct adaptation method when the indirect learning result is within a prescribed error tolerance, as such this method is closely related to the adaptive control methods. Also hash addressing technique, similar to the CMAC functional architecture, is introduced for partitioning network hidden nodes according to the system states, so global neuro control properties can be organized by the local ones. For uniform stability, the sliding mode control is introduced when the neural network has not sufficiently learned the system dynamics. With proper assumptions on the controlled system, global stability and tracking error convergence proof can be given. The performance of the proposed control scheme is demonstrated with the simulation results of a nonlinear system.

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Robust Deterministic Control of Singularly Perturbed Uncertain Systems (특이섭동 불확실시스템의 견실확정제어)

  • 강철구
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.6
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    • pp.1542-1550
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    • 1994
  • For a class of singularly perturbed uncertain system, an output feedback control law is designed. The controller structure is designed based on the uncertain reduced-order system, and the controller parameters are determined by information on the reduced-order and full-order systems. It has been shown that the reduces-order system with the designed controller possesses a stability property(specifically, a global uniform attractivity). Furthermore, the stability property of this control scheme is robust with respect to singular perturbation ; i.e., the full-order system, subject to the same controller, possesses the global uniform attractivity, provided the singular perturbation parameter $\mu<\mu^{*}$, where a threshold value $\mu^{*}$ can be computed from the information available on the full-order system.

STABILITY PROPERTIES OF A DELAYED VIRAL INFECTION MODEL WITH LYTIC IMMUNE RESPONSE

  • Song, Fang;Wang, Xia;Song, Xinyu
    • Journal of applied mathematics & informatics
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    • v.29 no.5_6
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    • pp.1117-1127
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    • 2011
  • In this paper, a class of more general delayed viral infection model with lytic immune response is proposed by Song et al.[1] ([Journal of Mathematical Analysis Application 373 (2011), 345-355). We derive the basic reproduction numbers $R_0$ and $R_0^*$ 0 for the viral infection, and establish that the global dynamics are completely determined by the values of $R_0$ and $R_0^*$. If $R_0{\leq}1$, the viral-free equilibrium $E_0$ is globally asymptotically stable; if $R_0^*{\leq}1$ < $R_0$, the immune-free equilibrium $E_1$ is globally asymptotically stable; if $R_0^*$ > 1, the chronic-infection equilibrium $E_2$ is globally asymptotically stable by using the method of Lyapunov function.

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
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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.

THE RULE OF TRAJECTORY STRUCTURE AND GLOBAL ASYMPTOTIC STABILITY FOR A FOURTH-ORDER RATIONAL DIFFERENCE EQUATION

  • Li, Xianyi;Agarwal, Ravi P.
    • Journal of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.787-797
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    • 2007
  • In this paper, the following fourth-order rational difference equation $$x_{n+1}=\frac{{x_n^b}+x_n-2x_{n-3}^b+a}{{x_n^bx_{n-2}+x_{n-3}^b+a}$$, n=0, 1, 2,..., where a, b ${\in}$ [0, ${\infty}$) and the initial values $X_{-3},\;X_{-2},\;X_{-1},\;X_0\;{\in}\;(0,\;{\infty})$, is considered and the rule of its trajectory structure is described clearly out. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is $1^+,\;1^-,\;1^+,\;4^-,\;3^+,\;1^-,\;2^+,\;2^-$ in a period, by which the positive equilibrium point of the equation is verified to be globally asymptotically stable.