• Journal of the Chungcheong Mathematical Society
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• 제30권3호
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• pp.323-329
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• 2017

In this paper, by rigorous calculations, we consider $L^2({\mathbb{R}})-spectrum$ of linear differential operators with periodic coefficients. These operators are usually seen in linearization of nonlinear partial differential equations about spatially periodic traveling wave solutions. Here, by using the solution operator obtained from Floquet theory, we prove rigorously that $L^2({\mathbb{R}})-spectrum$ of the linear operator is determined by the eigenvalues of Floquet matrix.

• Journal of the Chungcheong Mathematical Society
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• 제34권1호
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• pp.27-35
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• 2021

We study the existence of positive T-periodic solutions of ratio-dependent predator-prey systems with time periodic and spatially dependent coefficients. The fixed point theorem by H. Amann is used to obtain necessary and sufficient conditions for the existence of positive T-periodic solutions.

• Bulletin of the Korean Mathematical Society
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• 제47권5호
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• pp.889-905
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• 2010

In this paper, a distribution free approach to the parameter estimation of a simple bilinear model with periodic coefficients is presented. The proposed method relies on minimum distance estimator based on the autocovariances of the squared process. Consistency and asymptotic normality of the estimator, as well as hypotheses testing, are derived. Numerical experiments on simulated data sets are presented to highlight the theoretical results.

• Journal of the Korean Mathematical Society
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• 제48권2호
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• pp.223-240
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• 2011

In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.143-152
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• 2010

Based on the Exp-function method and a suitable transformation, new generalized solitonary solutions including free parameters of the MDI and Sawada-Kotera equations with variable coefficients are obtained, form which solitary wave solutions and periodic solutions including some known solutions reported in open literature are derived as special cases. The free parameters in the obtained generalized solitonary solutions might imply some meaningful results in the physical models. It is shown that the Exp-function method provides a very effective and important new method for nonlinear evolution equations with variable coefficients.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1381-1393
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• 2011

In this paper, we consider two-species periodic Gilpin-Ayala competition system with delay and impulsive effect. By using some analysis methods, sufficient conditions for the permanence of the system are derived. Further, we give the conditions of the existence and global asymptotic stable of positive periodic solution.

• Journal of the Chungcheong Mathematical Society
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• 제19권2호
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• pp.123-131
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• 2006

In this paper, a numerical programming for Liapunov index of differential equations with periodic coefficients depending on parameters is given. The associated equations are given at first, then existence of periodic solutions to the associated equations is proved in this paper. And we compute periodic solution u(t) of the associated equations. Finally, we give the error of approximate calculation.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.1031-1049
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• 2012

In this paper, a class of impulsive fuzzy bi-directional associative memory (BAM) neural networks with distributed delays and variable coefficients are considered. Using Lyapunov functional method and fixed point theorem, we derived some sufficient conditions for the existence and globally exponential stability of unique periodic solution of the networks. The results obtained are new and extend the previous known results. In addition, an example is given to show the effectiveness of our results obtained.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 한국소음진동공학회 2000년도 추계학술대회논문집
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• pp.443-448
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• 2000

In this paper, we propose a novel adaptive feedforward controller for periodic disturbance and noise cancellation, with a frequency tracking capability. It can be added to an existing feedback control system without altering the original closed-loop characteristics, which is based on adaptive algorithm. We introduce novel algorithm "Constrained AFC(adaptive feedforward controller) algorithm" that increase the convergence region regardless of the delay in the closed loop system. In the algorithms, coefficients of the controller are adapted using the residuals of constrained structure which are defined in such a way that the coefficients become time invariant. The proposed algorithm not only estimate the magnitude and phase of the tonal disturbance and noise but also track the frequency of the tone, which changes in quasi-static manner. The frequency tracking algorithm uses the instantaneous frequency approach based on Hilbert transform. A number of computer simulations have been carried out in order to demonstrate the effectiveness of proposed method under various conditions.

• Journal of Mechanical Science and Technology
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• 제20권12호
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• pp.2043-2051
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• 2006

This paper considered identification of vibration characteristics of flexible structure with vector channel periodic lattice filter. We present an algorithm for AR coefficients for the vector-channel lattice filters, and characteristic equation and transfer function are derived from these coefficients. Vibration lattice filter is then constructed from the vector channel lattice filter, and performance of this vibration filter is tested with a test signal which is a combination of many sine waves to compare the performance of scalar and vector channel lattice. Also it is applied to the cantilever data to identify properties of the system, such as natural frequencies and damping ratios, to show its performance.