• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.773-791
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• 2017

In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory on topological spaces under appropriate separation axioms. First, we discuss fundamental properties of attractors such as maximality and stability and establish some existence results. Then, we give a converse Lyapunov theorem. Finally, the Morse decomposition of attractors is also addressed.

• The Journal of the Convergence on Culture Technology
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• v.7 no.3
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• pp.353-358
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• 2021

This study provides the syntactic analysis for the agreement attraction by proposing three types of syntactic subject-verb agreement. Because subject-verb number agreement codifies the link between a predicate and its subject, it must be the purely syntactic processes of the head-to-head agreement or the feature percolation, where relevant agreement features percolate upward or downward through the hierarchical syntactic structure. The agreement errors are not affected by linear proximity or minimal interference, but instead are affected by the hierarchical relationship between an agreement target and a local attractor. The data in this paper includes the complex noun phrases with a modifier PP or a relative clause CP. Here, the [+PL] feature is suggested to be a local attractor for subject-verb agreement errors as a strong feature. Therefore, speakers tend to erroneously produce plural agreement for a singular subject in a main clause due to a plural NP in a modifier PP or plural agreement for a singular subject in a relative clause due to plural main subject.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.333-339
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• 2014

In this paper, we describe the characterizations of omega limit sets (= ${\omega}$-limit set) on $\mathbb{R}^2$ in detail. For a local real analytic flow ${\Phi}$ by z' = f(z) on $\mathbb{R}^2$, we prove the ${\omega}$-limit set from the basin of a given attractor is in the boundary of the attractor. Using the result of Jim$\acute{e}$nez-L$\acute{o}$pez and Llibre [9], we can completely understand how both the attractors and the ${\omega}$-limit sets from the basin.

• Water for future
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• v.27 no.3
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• pp.45-54
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• 1994

Basic theory of fractal dimension is introduced and performed for the generated time series using the water balance model. The water balance equation over a large area is analyzed at seasonal time scales. In the generation and modification of mesoscale circulation local recycling of precipitation and dynamic effects of soil moisture are explicitly included. Time delay is incorporated in the analysis. Depending on the parameter values, the system showed different senarios in the evolution such as fixed point, limit cycle, and chaotic types of behavior. The stochastic behavior of the generated time series is due to deterministic chaos which arises from a nonlinear dynamic system with a limited number of equations whose trajectories are highly sensitive to initial conditions. The presence of noise arose from the characterization of the incoming precipitation, destroys the organized structure of the attractor. The existence of the attractor although noise is present is very important to the short-term prediction of the evolution. The implications of this nonlinear dynamics are important for the interpretation and modeling of hydrologic records and phenomena.

• The KIPS Transactions:PartB
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• v.9B no.4
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• pp.421-428
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• 2002

The local prediction method utilizing embedding vector loses the prediction power when the parameter r estimation is not exact for predicting the chaos time series induced from the high order differential equation. In spite of the fact that there have been a lot of suggestions regarding how to estimate the delay time ($\tau$), no specific method is proposed to apply to any time series. The inclinded linear model, which utilizes inclinded netter, yields satisfying degree of prediction power without estimating exact delay time ($\tau$). The usefulness of this approach has been indicated not only theoretically but also in practical situation when the method w8s applied to economical time series analysis.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1101-1123
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• 2011

Numerical schemes are routinely used to predict the behavior of continuous dynamical systems. All such schemes transform flows into maps, which can possess dynamical behavior deviating from their continuous counterparts. Here the common bifurcations of scalar dynamical systems are transformed under a class of algorithms known as linearized one-point collocation methods. Through the use of normal forms, we prove that each such bifurcation in an originating flow gives rise to an exactly corresponding one in its discretization. The conditions for spurious period doubling behavior under this class of algorithm are derived. We discuss the global behavioral consequences of a singular set induced by the discretizing methods, including loss of monotonicity of solutions, intermittency, and distortion of attractor basins.

• KIEE International Transactions on Power Engineering
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• v.4A no.1
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• pp.18-25
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• 2004

This paper proposes a totally new method in the chaos characteristics' analysis of power systems, the introduction of topological invariants. Using a return histogram, a bifurcation graph was drawn. As well, the periodic orbits and topological invariants - the local crossing number, relative rotation rates, and linking number during the process of period-doubling bifurcation and chaos were extracted. This study also examined the effect on the topological invariants when the sensitive parameters were varied. In addition, the topological invariants of a three-dimensional embedding of a strange attractor were extracted and the result was compared with those obtained from differential equations. This could be a new approach to state detection and fault diagnosis in dynamical systems.

• Journal of Biosystems Engineering
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• v.25 no.2
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• pp.123-130
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• 2000

A forcasting scheme for daily solar irradiance on agricultural field sis proposed by application of chaos theory to a long term observation data. It was conducted by reconstruction of phase space, attractor analysis, and Lyapunov analysis. Using the methodology , it was determined whether evolution of the five climatic data such as daily air temperature , water temperature , relative humidity, solar radiation, and wind speed are chaotic or not. The climatic data were collected for three years by an automated weather station at Hwasung-gun, Kyonggi-province. The results showed that the evolution of solar radiation was chaotic , and could be predicted. The prediction of the evolution of the solar radiation data was executed by using ' local optimal linear reconstruction ' algorithm . The RMS value of the predicting for the solar radiation evolution was 4.32 MJ/$m^2$ day. Therefore, it was feasible to predict the daily solar radiation based on the chaos theory.

• Proceedings of the KIEE Conference
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• 2003.11a
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• pp.297-299
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• 2003

This paper proposes a totally new method in the chaos characteristics analysis of power systems, the introduction of topological invariants. Using a return histogram the bifurcation graph was drawn, the periodic orbits and topological invariants the local crossing number, relative rotation rates, and linking number during the process of period-doubting bifurcation and chaos were extracted. This study also examined the effect on the topological invariants when the sensitive parameters were varied. In addition, the topological invariants of a three-dimensional embedding of the strange attractor was extracted and the result was compared with those obtained from differential equations. This could be a new way for a state detection and fault diagnosis in a dynamical system.

• Journal of Agricultural Extension & Community Development
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• v.22 no.2
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• pp.135-144
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• 2015

Competitiveness has been associated in the tourism literature as a crucial factor for the success of tourist destinations. This study is to develop indicators that measure destination competitiveness of rural tourism townships in Korea. It was conducted via a Delphi technique and the analytical hierarchy process method. After four rounds of discussions, the panel members reached consensus on a set of 27 indicators with three dimensions which are attractor (resource, infrastructure, and tourism products), assistance (tourism business assistance and value-added processing assistance), and planning and management (planning for development, capacity for management). This set of destination competitiveness indicators can serve as a starting point for devising a set of indicators at the local level in order to be useful rural tourism sector manager and administrators. The selected indicators are measurable, demand driven and practical to show the real performance in rural destination.