• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.457-467
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• 2013

There exist many deterministic models for signaling pathways in systems biology. However the models do not consider the stochastic properties of the pathways, which means the models fit well with experimental data in certain situations but poorly in others. Incorporating stochasticity into deterministic models is one way to handle this problem. In this paper the way is used to produce stochastic models based on the deterministic differential equations for the published extracellular signal-regulated kinase (ERK) pathway. We consider strong convergence and stability of the numerical approximations for the stochastic models.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.11
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• pp.974-980
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• 2000

In this paper, we present a method that has flexibility of exact assignment of eigenstructure with the stochastic robustness for LTI(Linear-Time-Invariant) systems. The stochastic robustness of LTI systems is determined by the probability distributions of closed-loop eigenvalues. The probabilistic stability region is presented stochastically using the Monte Carlo evaluations. The proposed scheme is applied to designing a simple system and a flight control system with stochastic parameter variations to confirm the usefulness of the scheme.

• Structural Engineering and Mechanics
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• v.52 no.3
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• pp.525-540
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• 2014

The Lyapunov exponent and moment Lyapunov exponents of Hill's equation with frequency and damping coefficient fluctuated by correlated wideband random processes are studied in this paper. The method of stochastic averaging, both the first-order and the second-order, is applied. The averaged $It\hat{o}$ differential equation governing the pth norm is established and the pth moment Lyapunov exponents and Lyapunov exponent are then obtained. This method is applied to the study of the almost-sure and the moment stability of the stationary solution of the thin simply supported beam subjected to time-varying axial compressions and damping which are small intensity correlated stochastic excitations. The validity of the approximate results is checked by the numerical Monte Carlo simulation method for this stochastic system.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.11
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• pp.2066-2073
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• 2008

In this paper, the problem of global asymptotic stability of uncertain stochastic neural networks with delay is considered. The delay is assumed to be time-varying and belong to a given interval. Based on the Lyapunov stability theory, new delay-dependent stability criteria for the system is derived in terms of LMI(linear matrix inequality). Three numerical examples are given to show the effectiveness of proposed method.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.11-31
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• 2023

The paper presents a critical analysis of selected topics related to the modeling of interacting species in which prey has nonlinear reproduction, which is in competition with predator. The mathematical model's stochastic stability is investigated. The method of designing appropriate Lyapunov functions is used to identify permanence conditions among the parameters of the model and conditions for the structure to no longer be extinct. The system's two-dimensional diffusive stability is regarded and studied. The system experiences the process of saddle-node bifurcation by varying the death rate of predator parameter. Further effects of parameters that undergo inherent oscillations are numerically investigated, revealing that as the intensity of predation parameter b is increased, the device encounters non-periodic and damped oscillations.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.967-982
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• 2023

The goal of this study is to derive a class of random impulsive non-local fractional stochastic differential equations with finite delay that are of Caputo-type. Through certain constraints, the existence of the mild solution of the aforementioned system are acquired by Kransnoselskii's fixed point theorem. Furthermore through Ito isometry and Gronwall's inequality, the Hyers-Ulam stability of the reckoned system is evaluated using Lipschitz condition.

• Journal of Electrical Engineering and Technology
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• v.11 no.1
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• pp.200-214
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• 2016

This paper investigates the problem of stability analysis and robust H_∞ controller for time-delayed systems with parameter uncertainties and stochastic disturbances. It is assumed parameter uncertainties are norm bounded and mean and variance for disturbances of them are known. Firstly, by constructing a newly augmented Lyapunov-Krasovskii functional, a stability criterion for nominal systems with time-varying delays is derived in terms of linear matrix inequalities (LMIs). Secondly, based on the result of stability analysis, a new controller design method is proposed for the nominal form of the systems. Finally, the proposed method is extended to the problem of robust H_∞ controller design for a time-delayed system with parameter uncertainties and stochastic disturbances. To show the validity and effectiveness of the presented criteria, three examples are included.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.20 no.5
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• pp.457-462
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• 1987

Stochastic stability criterias for ocean wave analysis add simulation are studied using the data simulated by the linear superposition method. To clarify the criterias, the effects of the simulation parameters on the variance of stochastic properties of ocean waves are investigated, and the stable conditions of the parameters are estimated through the comparative study on the stochastic properties of simulated waves and well-known ocean waves. The simulation parameters considered are high frequency cut-off, data length, and number and phase angle of component waves. Statistical characteristics analysed are wave height, period and steepness, and the formation of groups of higher waves, resonance periods, steeper higher waves and extreme run-length of the run.

• 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.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.985-999
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• 2018

This paper is devoted to the existence and uniqueness of $L^p$ (p > 1) solutions for general time interval multidimensional backward stochastic differential equations (BSDEs for short), where the generator g satisfies a ($p{\wedge}2$)-order weak monotonicity condition in y and a Lipschitz continuity condition in z, both non-uniformly in t. The corresponding stability theorem and comparison theorem are also proved.