• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.685-699
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• 2019

This research is focused on a continuous epidemic model of transmission of Plasmodium vivax malaria with a time delay. The model is represented as a system of ordinary differential equations with delay. There are two equilibria, which are the disease-free state and the endemic equilibrium, depending on the basic reproduction number, $R_0$, which is calculated and decreases with the time delay. Moreover, the disease-free equilibrium is locally asymptotically stable if $R_0<1$. If $R_0>1$, a unique endemic steady state exists and is locally stable. Furthermore, Hopf bifurcation is applied to determine the conditions for periodic solutions.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.111-137
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• 2021

Higson proved that every homotopy invariant, stable and split exact functor from the category of C⁎-algebras to an additive category factors through Kasparov's KK-theory. By adapting a group equivariant generalization of this result by Thomsen, we generalize Higson's result to the inverse semigroup and locally compact, not necessarily Hausdorff groupoid equivariant setting.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.343-348
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• 2007

In this paper, we show that if a homeomorphism has the pseudo-orbit-tracing-property and its nonwandering set is locally connected, then the limit sets of wandering points whose stable sets have nonempty interior consist of single periodic orbit.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.871-878
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• 2010

In this paper, we show that if a homeomorphism has the pseudo-orbit-tracing-property and its nonwandering set is locally connected, then the points whose stable sets have nonempty interior are periodic points.

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.65-74
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• 1992

In this note, we show that the ${\omega}$-limit mapping is continuous and the Lipschitz constants vary continuously if the flow (x, ${\pi}$) is Lipschitz stable. Moreover we analyse the ${\omega}$-limit sets under the generalized locally Lipschitz stable flows.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.7
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• pp.29-36
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• 1998

In this paper we propose a control law using a Lyapunov-like function that makes stable the systems which have mis-matched uncertainties. The existing control law using a Lyapunov-like function, which gives global saymptotic stability, is designed under the assumption of a targetsystem to be stable locally. But we broaden here the class of target systems by designing the control law which can give uniform ultimate boundedness to even the systems not satisfing the locally asymptotic stability. And we also show that the control law giving global asymptotic stability can be designed more systematically through using the uniform ultimate boundedness.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.287-300
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• 2020

We introduce and study notions of expansivity, topological stability and persistence for Borel measures with respect to time varying bi-measurable maps on metric spaces. We prove that on Mandelkern locally compact metric spaces expansive persistent measures are topologically stable in the class of all time varying homeomorphisms.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1393-1407
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• 2023

In this study, we propose a dynamic SEIQRV mathematical model and examine it to comprehend the dynamics of COVID-19 pandemic transmission in the Coimbatore district of Tamil Nadu. Positiveness and boundedness, which are the fundamental principles of this model, have been examined and found to be reliable. The reproduction number was calculated in order to predict whether the disease would spread further. Existing arrangements of infection-free, steady states are asymptotically stable both locally and globally when R₀ < 1. The consistent state arrangements that are present in diseases are also locally steady when R₀ < 1 and globally steady when R₀ > 1. Finally, the numerical data confirms our theoretical study.

• Proceedings of the KIEE Conference
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• 1990.11a
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• pp.407-412
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• 1990

This note presents a novel algorithm for a continuous-time direct adaptive pole placement control for single-input single-out nonminimum phase systems. Although the resulting overall closed-loop system is locally stable, assumptions about parameter convergence or the nature of the external input are not considered.

• Proceedings of the Korean Information Science Society Conference
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• 2002.04b
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• pp.289-291
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• 2002

Host of source separation methods focus on stationary sources so higher-order statistics is necessary In this paler we consider a problem of source separation when sources are second-order nonstationary stochastic processes . We employ the natural gradient method and develop learning algorithms for both 1inear feedback and feedforward neural networks. Thus our algorithms possess equivariant property Local stabi1iffy analysis shows that separating solutions are always locally stable stationary points of the proposed algorithms, regardless of probability distributions of