• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.363-374
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• 2007

In this paper, we consider the discrete nonlinear delay model which describe the control of a single population of cells. We establish a sufficient condition for oscillation of all positive solutions about the positive equilibrium point and give a sufficient condition for the global attractivity of the equilibrium point. The oscillation condition guarantees the prevalence of the population about the positive steady sate and the global attractivity condition guarantees the nonexistence of dynamical diseases on the population.

• 대한수학회보
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• 제40권3호
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• pp.489-501
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• 2003

In this paper we shall consider the nonlinear delay difference equation $\Delta({p_n}{\Deltax_N})\;+\;q_nf(x_{n-\sigma})\;=\;0,\;n\;=\;0,\;1,\;2,\;...$ when (equation omitted). We will establish some sufficient conditions which guarantee that every solution is oscillatory or converges to zero.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.581-589
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• 2009

In this paper, we are concerned with a class of nonlinear second-order differential equations with a nonlinear damping term and forcing term: $$(r(t)k_1(x(t),x'(t)))'+p(t)k_2(x(t),x'(t))x'(t)+q(t)f(x(t))=0$$. Passage to more general class of equations allows us to remove a restrictive condition usually imposed on the nonlinearity. And, as a consequence, our results apply to wider classes of nonlinear differential equations. Some illustrative examples are considered.

• 전자공학회논문지C
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• 제35C권5호
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• pp.41-49
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• 1998

This paper deals with the self-excited oscillation of a system that is controlled by a dynamic nonlinear fuzzy controller. The self-excited oscillation can be observed in the systems composed of nonlinear elements and its analysis is as important as that of stability in the design of nonlinear systems. by using the frequency transfer function analysis known as the describing function method in nonlinear control theory, the oscillation is theoretically predicted. First, the describing function of a dynamic fuzzy controller is derived and then, based on the derived describing fuction, self-excited oscillation of the system controlled by a dynamic fuzzy controller is predicted. To obtain the describing function of the dynamic fuzzy controller, a simple structure is assumed for the fuzzy controller.

• Journal of Advanced Marine Engineering and Technology
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• 제26권1호
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• pp.116-124
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• 2002

The bubble model by Keller and Prosperetti is adapted to solve the nonlinear oscillation of a gas bubble. This formulation leads to accurate results since it introduces the energy equation instead of the polytropic assumption for the bubble interior. The numerical method used in this study is stable enough to handle large amplitude of bubble oscillation. The numerical results show some interesting nonlinear phenomena fur the bubble oscillator. The excitation changes the natural frequency of the bubble and makes some harmonic resonances at $f/f_0=1/2, 1/3$ and so on. The natural frequency of a bubble oscillator decreases compared with the linear case result, which means that the nonlinear bubble oscillation system is a "softening"system. In addition, the frequency response curve jumps up or down at a certain frequency. It is also found that there exist multi-valued regions in the frequency response curve depending on the initial conditions of bubble. The dependency of the bubble motion on the initial condition can generate extremely large pressure and temperature which might be the cause of the acoustic cavitation and the sonoluminescence.inescence.

• 전기전자학회논문지
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• 제6권2호
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• pp.128-135
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• 2002

선형 플랜트의 극한 이득과 주기를 찾기 위해 포화함수를 이용하여 자기 진동을 발생 시켰다. 포화함수 사용으로 극한이득과 주기의 정확성을 높였다. 발견한 극한 이득과 극한 주기는 PID 제어기 값을 구하는데 사용하였다. 정적인 부하 왜란 등이 있는 경우 비대칭 진동이 발생할 수 있다. 발생하는 비대칭 자기 진동을 분석하였고 분석결과로부터 극한 이득과 주기를 찾는 방법을 제안하였다.

• 대한수학회논문집
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• 제19권3호
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• pp.495-506
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• 2004

Some oscillation criteria are given for second order nonlinear differential equations by means of integral averaging technique.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.125-138
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• 2003

Some Riccati type difference inequalities are established for the second-order nonlinear difference equations with negative neutral term $\Delta$(a(n)$\Delta$(x(n) - px(n-$\tau$))) + f(n, x($\sigma$(n))) = 0 using these inequalities we obtain some oscillation criteria for the above equation.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.447-454
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• 2014

Two necessary and sufficient conditions for the oscillation of the bounded solutions of the second-order nonlinear delay differential equation $$(a(t)x^{\prime}(t))^{\prime}+q(t)f(x[{\tau}(t)])=0$$ are obtained by constructing the sequence of functions and using inequality technique.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 춘계학술대회논문집A
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• pp.585-590
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• 2000

Problems involved in the numerical analysis on the forced oscillation of nonlinear oscillators such a microbubble oscillation under ultrasound and Duffing oscillator were discussed. One of the problems is proper choice of the time scale of the driving force. which is related to the numerical artifacts due to the mismatch between the natural frequency of an oscillator(or bubble) and the characteristic frequency of the applied force. Such problem may occur in a nonlinear oscillator whose behavior is crucially dependent on the frequency of the applied force. The artificial resonance problem during the numerical evaluation of such nonlinear systems was also discussed.