• Journal of the Korean Data and Information Science Society
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• v.21 no.3
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• pp.597-603
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• 2010

We obtain, in using generalized norms, some stability results for a very general system of di erential equations using the method of cone-valued Lyapunov funtions and we obtain necessary and/or sufficient conditions for the uniformly asymptotic stability of the nonlinear differential system.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.429-436
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• 2003

We study the asymptotic equivalence between the nonlinear differential system $\chi$'(t) = f(t, $\chi$(t)) and its variational system ν'(t) = f$\chi$(t, 0)ν(t) by using the comparison principle and notion of strong stability.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.592-597
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• 2003

In this paper, some differential geometric conditions for the observer using a recurrent neural network are provided in terms of a stochastic nonlinear system control. In the stochastic nonlinear system, it is necessary to make an additional condition for observation of stochastic nonlinear system, called perfect filtering condition. In addition, we provide a observer using a recurrent neural network for the observation of a stochastic nonlinear system with the proposed observation conditions. Computer simulation shows that the control performance of the stochastic nonlinear system with a observer using a recurrent neural network satisfying the proposed conditions is more efficient than the conventional observer as Kalman filter

• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.11-21
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• 2014

The present paper is concerned with the notions of Lipschitz and asymptotic stability for perturbed nonlinear differential system knowing the corresponding stability of nonlinear differential system. We investigate Lipschitz and asymtotic stability for perturbed nonlinear differential systems. The main tool used is integral inequalities of the Bihari-type, in special some consequences of an extension of Bihari's result to Pinto and Pachpatte, and all that sort of things.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.545-556
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• 2009

We show that two notions of asymptotic equilibrium and asymptotic equilibrium in variation for nonlinear differential systems are equivalent via $t_{\infty}$-similarity of associated variational systems. Moreover, we study the asymptotic equivalence between nonlinear system and its variational system.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.877-894
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• 2013

In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green's function, a nonlinear alternative of Leray-Schauder type, Guo-Krasnoselskii's fixed point theorem in a cone. Some examples are included to show the applicability of our results.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.605-613
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• 2013

In this paper, we investigate bounds for solutions of perturbed nonlinear differential systems.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.383-389
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• 2010

In this paper, we investigate h-stability of the nonlinear differential systems using the notion of $t_{\infty}$-similarity.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.827-834
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• 2010

In this paper, we investigate h-stability of the nonlinear perturbed differential systems.

• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.259-270
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• 2017

The stochastic vibration response of the sandwich beam with the nonlinear adjustable visco-elastomer core and supported mass under stochastic support motion excitations is studied. The nonlinear dynamic properties of the visco-elastomer core are considered. The nonlinear partial differential equations for the horizontal and vertical coupling motions of the sandwich beam are derived. An analytical solution method for the stochastic vibration response of the nonlinear sandwich beam is developed. The nonlinear partial differential equations are converted into the nonlinear ordinary differential equations representing the nonlinear stochastic multi-degree-of-freedom system by using the Galerkin method. The nonlinear stochastic system is converted further into the equivalent quasi-linear system by using the statistic linearization method. The frequency-response function, response spectral density and mean square response expressions of the nonlinear sandwich beam are obtained. Numerical results are given to illustrate new stochastic vibration response characteristics and response reduction capability of the sandwich beam with the nonlinear visco-elastomer core and supported mass under stochastic support motion excitations. The influences of geometric and physical parameters on the stochastic response of the nonlinear sandwich beam are discussed, and the numerical results of the nonlinear sandwich beam are compared with those of the sandwich beam with linear visco-elastomer core.