• Journal of the Korean Mathematical Society
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• v.49 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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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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• v.26 no.4
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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.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.7
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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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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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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• v.17 no.1_2_3
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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.

• Journal of the Korean Geographical Society
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• v.49 no.3
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• pp.371-389
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• 2014

This study aims to analyze the redistricting problems in non-autonomous Gu. Although non-autonomous Gu is a just local administrative district, it has been regarded as an important and basic spatial unit in electoral redistricting. By the reform of Public Official Election Act in 2012, however, non-autonomous Gu is distinguished from local governments like Si, Gun and autonomous Gu, in boundary delimitation for the 19th National Assembly election, and some are divided into a part of another constituency. About these background, this study points out the following problems. First, in national scale, the reform of Act made the malapportionment in constituencies of non-autonomous Gus, comparing with those of local governments. Second, there was the discriminative application of Act in each non-autonomous Gu and it will make the malapportionment worse in next election, considering the reorganization of local administrative system. Finally, this study propose that it is necessary to select one from a variety of redistricting principles, especially between the prevention of gerrymandering, the representativeness of local government and the apportionment, prior to another amendment of redistricting system and the debate about political reform.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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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.

• Korean Journal of Artificial Intelligence
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• v.12 no.3
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• pp.9-15
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• 2024

This paper addresses the critical need for quadcopters in GPS-denied indoor environments by proposing a novel attitude control mechanism that enables autonomous navigation without external guidance. Utilizing AR marker detection integrated with a dual PID controller algorithm, this system ensures accurate maneuvering and positioning of the quadcopter by compensating for the absence of GPS, a common limitation in indoor settings. This capability is paramount in environments where traditional navigation aids are ineffective, necessitating the use of quadcopters equipped with advanced sensors and control systems. The actual position and location of the quadcopter is achieved by AR marker detection technique with the image processing system. Moreover, in order to enhance the reliability of the attitude PID control, the dual closed loop control feedback PID control with dual update periods is suggested. With AR marker detection technique and autonomous attitude control, the proposed quadcopter system decreases the need of additional sensor and manual manipulation. The experimental results are demonstrated that the quadrotor's autonomous attitude control and operation with the dual closed loop control feedback PID controller with hierarchical (inner-loop and outer-loop) command update period is successfully performed under the non-GPS aided indoor environment and it enhanced the reliability of the attitude and the position PID controllers within 17 seconds. Therefore, it is concluded that the proposed attitude control mechanism is very suitable to GPS-denied indoor environments, which enables a quadcopter to autonomously navigate and hover without external guidance or control.