• 대한수학회지
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• 제49권4호
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• pp.703-713
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• 2012

In this paper we study ${\omega}$-limit sets and attraction of non-autonomous discrete dynamical systems. We introduce some basic concepts such as ${\omega}$-limit set and attraction for non-autonomous discrete system. We study fundamental properties of ${\omega}$-limit sets and discuss the relationship between ${\omega}$-limit sets and attraction for non-autonomous discrete dynamical systems.

• 대한수학회논문집
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• 제17권1호
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• pp.155-163
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• 2002

The purpose of this paper is to establish discrete versions of the well-known Lyapunov's stability theorem and LaSalle's invariance theorem for a non-autonomous discrete dynamical system. Our proofs for these theorems are constructive in the sense that they are made by explicitly building a Lyapunov function for the system. A comparison between non-autonomous discrete dynamical systems and continuous dynamical systems is conducted.

• Korean Journal of Mathematics
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• 제26권4호
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• pp.583-599
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• 2018

In this paper, we are concerned with the existence of random dynamics for stochastic non-autonomous reaction-diffusion equations driven by a Wiener-type multiplicative noise defined on the unbounded domains.

• 제어로봇시스템학회논문지
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• 제6권7호
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• pp.586-593
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• 2000

In this paper we propose a new approach to the autonomous wall-following of wheeled mobile robots using hybrid system reference motion synthesis and generation. The hybrid system approach is in-troduced to the motion control of nonholonomic mobile robots for the indoor navigation problems. In the dis-crete event system the discrete states are defined by the user-defined constraints and the reference mo-tion commands are specified in the abstracted motions. The hybrid control system applied for the non-holonomic mobile robots can combine the motion planning and autonomous navigation with obstacle avoid-ance for the indoor navigation problem. Simulation results show that hybrid system approach is an effective method for the autonomous navigation in indoor environments.

• 대한수학회보
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• 제51권2호
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• pp.457-478
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• 2014

In this paper, a 3D autonomous system, which has only stable or non-hyperbolic equilibria but still generates chaos, is presented. This system is topologically non-equivalent to the original Lorenz system and all Lorenz-type systems. This motivates us to further study some of its dynamical behaviors, such as the local stability of equilibrium points, the Lyapunov exponent, the dissipativity, the chaotic waveform in time domain, the continuous frequency spectrum, the Poincar$\acute{e}$ map and the forming mechanism for compound structure of its special cases. Especially, with the help of the Project Method, its Hopf bifurcation of codimension one is in detailed formulated. Numerical simulation results not only examine the corresponding theoretical analytical results, but also show that this system possesses abundant and complex dynamical properties not solved theoretically, which need further attention.

• 대한수학회논문집
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• 제22권3호
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• pp.465-474
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• 2007

With the help of the coincidence degree and the related continuation theorem, we explore the existence of at least two periodic solutions of a discrete time non-autonomous ratio-dependent predator-prey system with control. Some easily verifiable sufficient criteria are established for the existence of at least two positive periodic solutions.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.195-215
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• 2005

In this paper, we investigate the dynamics of the mathematical model of two non-interacting preys in presence of their common natural enemy (predator) based on the non-autonomous differential equations. We establish sufficient conditions for the permanence, extinction and global stability in the general non-autonomous case. In the periodic case, by means of the continuation theorem in coincidence degree theory, we establish a set of sufficient conditions for the existence of a positive periodic solutions with strictly positive components. Also, we give some sufficient conditions for the global asymptotic stability of the positive periodic solution.

• 대한지리학회지
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• 제49권3호
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• pp.371-389
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• 2014

이 연구는 '자치구가 아닌 구', 즉 일반구의 선거구획정에서 발생한 그리고 발생할 문제를 분석하는 것이다. 행정구역으로서 일반구는 분명 지방자치단체에 해당되지 않지만, 정부수립 이후 최근까지 여러 공직선거의 선거구획정에 있어 중요한 공간단위로 간주되어 왔다. 하지만 2012년 개정된 '공직선거법'은 투표가치에 대한 평등원칙을 보장하겠다는 이유로 자치구 시 군과는 다르게 일반구에서만 그 일부 지역을 분할 편입시키는 것을 가능하게 했고, 실제 몇몇 일반구에 적용되었다. 동법을 기초로 진행된 제19대 총선을 사례로, 이 연구는 첫째 분할 편입된 일반구 선거구는 기초자치단체 선거구와 비교했을 때 개별 도시 스케일에서는 투표등가치성이 일부 보완되었지만 전국 스케일에서는 오히려 상당히 훼손되었고, 둘째 동일한 일반구 중에서도 분할 편입은 차별적으로 적용 진행되었으며, 이러한 동법 개정과 적용의 차별은 지방행정체제 개편을 고려하면 다음 선거에서는 더욱더 심각한 투표등가치성 훼손을 발생시키게 될 것임을 지적한다. 마지막으로 최근 일반구의 선거구획정을 비롯한 현행 선거구획정 제도와 과정들이 우리정치의 개혁 대상으로 인식되면서 다양한 대안들이 제시되고 있지만, 이 연구는 투표평등권 지역대표성 게리맨더링의 방지 등 서로 충돌하는 여러 선거구획정 원칙과 가치 중에서 우선될 것을 선택하는 논의가 먼저 이루어져야 하고, 그것이 일반구 선거구획정에서 발생하는 문제를 푸는 실마리가 될 것이라고 주장한다.

• 충청수학회지
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• 제33권2호
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• pp.237-253
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• 2020

This article studies asymptotic stability of non-auto nomous linear systems with time-dependent coefficient matrices {A(t)}_t∈ℝ. The classical theorem of Levinson has been widely used to science and engineering non-autonomous systems, but systems with defective eigenvalues could not be covered because such a family does not allow continuous diagonalization. We study systems where the family allows to have upper triangulation and to have defective eigenvalues. In addition to the wider applicability, working with upper triangular matrices in place of Jordan form matrices offers more flexibility. We interpret our and earlier works including Levinson's theorem from the perspective of invariant manifold theory.

• 자동차안전학회지
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• 제14권4호
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• pp.106-112
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• 2022

The purpose of this study is to explore ways of improving the motor vehicles safety certification system in preparation for the deployment of Lv.4 or higher autonomous vehicles. In order to effectively achieve the objectives of this study, theoretical and empirical research methodologies were employed, including literature review of prior research, government-published data, etc.; comparative research on legislative cases of other countries regarding motor vehicles safety certification; historical and legal research on domestic systems; legal analysis to explore approaches for improvement, etc. Some argue that the type approval system is needed in preparation for deploying autonomous vehicles, but there are several limitations in moving to the type approval system from the self-certification system currently adopted in Korea. First, there is a possibility that the system may be in conflict with the Korea-U.S. MOU regarding Foreign Motor Vehicles (1988) and the Korea-U.S. FTA (2011); second, there is a risk of undermining the cause of the self-certification system, which is the autonomy of manufacturers; third, the boundary between autonomous vehicles and non-autonomous vehicles is unclear; and fourth, the type approval system may hinder technological competitiveness. On the other hand, considering that the Korea-U.S. FTA and the UNECE IWVTA recognize exceptions to deal with road safety and risks to human health or the environment, and have a pre-certification system for some auto parts such as pressure-resistant containers, it can be said that there is room to introduce the type approval system for supplementation purposes. To improve the motor vehicles safety certification system while ensuring the safety of autonomous vehicles of Lv.4 or higher, the targets of type approval should be defined and the criteria, procedures, etc. for type approval should be established. At the same time, the consistency between motor vehicle-related laws and harmonization with international standards need to be considered.