• Title, Summary, Keyword: Volterra difference system

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h-STABILITY IN VOLTERRA DIFFERENCE SYSTEMS

  • Goo, Yoon Hoe;Park, Gyeong In;Ko, Jung Hyun
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.3
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    • pp.535-543
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    • 2009
  • We investigate h-stability of solutions of nonlinear Volterra difference systems and linear Volterra difference systems.

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STABILITY IN VARIATION FOR NONLINEAR VOLTERRA DIFFERENCE SYSTEMS

  • Choi, Sung-Kyu;Koo, Nam-Jip
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.101-111
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    • 2001
  • We investigate the property of h-stability, which is an important extension of the notions of exponential stability and uniform Lipschitz stability in variation for nonlinear Volterra difference systems.

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ASYMPTOTIC EQUIVALENCE OF VOLTERRA DIFFERENCE SYSTEMS

  • Choi, Sung Kyu;Kim, Jin Soon;Koo, Namjip
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.3
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    • pp.311-320
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    • 2007
  • We obtain a discrete analogue of Nohel's result in [5] about asymptotic equivalence between perturbed Volterra system and unperturbed system.

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BOUNDEDNESS OF DISCRETE VOLTERRA SYSTEMS

  • Choi, Sung-Kyu;Goo, Yoon-Hoe;Koo, Nam-Jip
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.663-675
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    • 2007
  • We investigate the representation of the solution of discrete linear Volterra difference systems by means of the resolvent matrix and fundamental matrix, respectively, and then study the boundedness of the solutions of discrete Volterra systems by improving the assumptions and the proofs of Medina#s results in [6].

On the Dynamics of Multi-Dimensional Lotka-Volterra Equations

  • Abe, Jun;Matsuoka, Taiju;Kunimatsu, Noboru
    • 제어로봇시스템학회:학술대회논문집
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    • pp.1623-1628
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    • 2004
  • In the 3-dimensional cyclic Lotka-Volterra equations, we show the solution on the invariant hyperplane. In addition, we show the existence of the invariant hyperplane by the center manifold theorem under the some conditions. With this result, we can lead the hyperplane of the n-dimensional cyclic Lotka-Volterra equaions. In other section, we study the 3- or 4-dimensional Hamiltonian Lotka-Volterra equations which satisfy the Jacobi identity. We analyze the solution of the Hamiltonian Lotka- Volterra equations with the functions called the split Liapunov functions by [4], [5] since they provide the Liapunov functions for each region separated by the invariant hyperplane. In the cyclic Lotka-Volterra equations, the role of the Liapunov functions is the same in the odd and even dimension. However, in the Hamiltonian Lotka-Volterra equations, we can show the difference of the role of the Liapunov function between the odd and the even dimension by the numerical calculation. In this paper, we regard the invariant hyperplane as the important item to analyze the motion of Lotka-Volterra equations and occur the chaotic orbit. Furtheremore, an example of the asymptoticaly stable and stable solution of the 3-dimensional cyclic Lotka-Volterra equations, 3- and 4-dimensional Hamiltonian equations are shown.

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Parameter Identification of Nonlinear Dynamic Systems using Frequency Domain Volterra model (비선형 동적 시스템의 파라미터 산정을 위한 주파수 영역 볼테라 모델의 이용)

  • Paik, In-Yeol;Kwon, Jang-Sub
    • Journal of the Earthquake Engineering Society of Korea
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    • v.9 no.3
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    • pp.33-42
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    • 2005
  • Frequency domain Volterra model is applied to nonlinear parameter identification procedure for dynamic systems modeled by nonlinear function. The frequency domain Volterra kernels, which correspond io linear, quadratic, and cubic transfer functions in lime domain, are incorporated in nonlinear parametric identification procedure. The nonlinear transfer functions, which can be derived from the Volterra series representation of the nonlinear differential equation of the system by Schetzen's method(1980), are directly used for modeling input output relation. The error is defined by the difference between the observed output and the estimated output which is calculated by substituting the observed input to nonlinear frequency domain model. The system parameters are searched by minimizing the error. Volterra model guarantees enough accuracy and convergence and the estimated coefficients have a good agreement with their actual values not only in the linear frequency region but also in the legion where the $2^{nd}\;or\;3^{rd}$ order nonlinearity is dominant.