• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2004.05a
• /
• pp.100-105
• /
• 2004

In this paper, we propose a method to avoid obstacles that have unstable limit cycles in a chaos trajectory surface. We assume all obstacles in the chaos trajectory surface have a Van der Pol equation with an unstable limit cycle. When a chaos robot meets an obstacle in a Lorenz equation or Hamilton equation trajectory, the obstacle reflects the robot. We also show computer simulation results for avoidance obstacle which fixed obstacles and hidden obstacles of Lorenz equation and Hamilton equation chaos trajectories with one or more Van der Pol obstacles

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.8 no.8
• /
• pp.1692-1699
• /
• 2004

In this paper, we propose a method to avoid obstacles that have unstable limit cycles in a chaos trajectory surface. We assume all obstacles in the chaos trajectory surface have a Van der Pol equation with an unstable limit cycle. We also show computer simulation results of Arnold equation, Chua's equation, Hyper-chaos equation, Hamilton equation and Lorenz chaos trajectories with one or more Van der Pol obstacles.

• Kyungpook Mathematical Journal
• /
• v.56 no.3
• /
• pp.647-655
• /
• 2016

Let H be a graph, and $k{\geq}{\chi}(H)$ an integer. We say that H has a cyclic Gray code of k-colourings if and only if it is possible to list all its k-colourings in such a way that consecutive colourings, including the last and the first, agree on all vertices of H except one. The Gray code number of H is the least integer $k_0(H)$ such that H has a cyclic Gray code of its k-colourings for all $k{\geq}k_0(H)$. For complete bipartite graphs, we prove that $k_0(K_{\ell},r)=3$ when both ${\ell}$ and r are odd, and $k_0(K_{\ell},r)=4$ otherwise.

• Proceedings of the Korea Inteligent Information System Society Conference
• /
• 2005.11a
• /
• pp.197-204
• /
• 2005

In this paper, we propose a method to an obstacle avoidance of chaotic robots that have unstable limit cycles in a chaos trajectory surface in the ubiquitous environment. We assume all obstacles in the chaos trajectory surface have a Van der Pol equation with an unstable limit cycle. We also show computer simulation results of Chua's equation, Lorenz equation, Hamilton and Hyper-chaos equation trajectories with one or more Van der Pol as an obstacles. We proposed and verified the results of the method to make the embedding chaotic mobile robot to avoid with the chaotic trajectory in any plane.

• Structural Engineering and Mechanics
• /
• v.34 no.4
• /
• pp.507-523
• /
• 2010

Parametric and forced non-linear vibrations of an axially moving rotor both in non-resonance and near-resonance cases have been investigated analytically in this paper. The axial speed is assumed to involve a mean value along with small harmonic fluctuations. Hamilton's principle is employed for this gyroscopic system to derive three coupled non-linear equations of motion. Longitudinal inertia is neglected under the quasi-static stretch assumption and two integro-partial-differential equations are obtained. With introducing a complex variable, the equations of motion is presented in the form of a single, complex equation. The method of multiple scales is applied directly to the resulting equation and the approximate closed-form solution is obtained. Stability boundaries for the steady-state response are formulated and the frequency-response curves are drawn. A number of case studies are considered and the numerical simulations are presented to highlight the effects of system parameters on the linear and nonlinear natural frequencies, mode shapes, limit cycles and the frequency-response curves of the system.