Slow passage through multiple bifurcation points

Do, Younghae,M. Lopez, Juan American Institute of Mathematical Sciences 2013 Discrete and continuous dynamical systems. Series Vol.18 No.1

Impulsive Perturbations of a Three-Species Food Chain System with the Beddington-DeAngelis Functional Response

Do, Younghae,Baek, Hunki,Kim, Dongseok Hindawi Limited 2012 Discrete dynamics in nature and society Vol.2012 No.-

<P>The dynamics of an impulsively controlled three-species food chain system with the Beddington-DeAngelis functional response are investigated using the Floquet theory and a comparison method. In the system, three species are prey, mid-predator, and top-predator. Under an integrated control strategy in sense of biological and chemical controls, the condition for extinction of the prey and the mid-predator is investigated. In addition, the condition for extinction of only the mid-predator is examined. We provide numerical simulations to substantiate the theoretical results.</P>

Stability of attractors formed by inertial particles in open chaotic flows

Younghae Do,Ying-Cheng Lai,Hun Ki Baek 한국산업응용수학회 2005 한국산업응용수학회 학술대회 논문집 Vol.- No.-

Particles having finite mass and size advected in open chaotic flows can form attractors behind structures. Depending on the system parameters, the attractors can be chaotic or nonchaotic. But, how robust are these attractors? In particular, will small, random perturbations destroy the attractors? Here, we address this question by utilizing a prototype flow system: a cylinder in a two-dimensional incompressible flow, behind which the von Karman vortex street forms. We find that attractors formed by inertial particles behind the cylinder are fragile in that they can be destroyed by small, additive noise. However, the resulting chaotic transient can be superpersistent in the sense that its lifetime obeys an exponential-like scaling law with the noise amplitude, where the exponent in the exponential dependence can be large for small noise. This happens regardless of the nature of the original attractor, chaotic or nonchaotic. We present numerical evidence and a theory to explain this phenomenon. Our finding makes direct experimental observation of superpersistent chaotic transients feasible and it also has implications for problems of current concern such as the transport and trapping of chemically or biologically active particles in large-scale flows.

Stability of fixed points on piecewise smooth systems

Younghae Do 한국산업응용수학회 2005 한국산업응용수학회 학술대회 논문집 Vol.- No.-

The stability type of fixed points of continuously differential dynamical systems can be determined by their Jacobian information. But in practical situation, we often meet piecewise smooth maps with a border separating two smooth regions. The discontinuous change in the Jacobian elements results in many atypical bifurcation phenomena, which is called border collision bifurcations, for instance a periodic orbit turning directly into a chaotic orbit, or multiple attractors coming into existence or going out of existence as the parameter is varied across some critical bifurcation value, etc. Recent research has shown the new type of border collision bifurcations, which is called the dangerous border collision bifurcations where a fixed point remains stable at both sides of the critical bifurcation point, but the orbit becomes unbounded at the critical point of bifurcation. Possibility for occurring such dangerous border collision bifurcations has been pointed out through numerical exploration but the mechanism causing its occurrence is not yet known. In the present paper, we focus on determining the stability type of fixed points of piece￢wise smooth systems. Specifically, consider non-differentiable fixed points which are located exactly on the border. In order to investigate the behavior of trajectories on piecewise linear systems having such fixed points, we consider the angle dynamics of the circle map defined on the unit circle with the assigned dilation ratios generated by the original piecewise linear system. From dynamical features of the circle map on the unit circle, we can measure the stability type of fixed points, which can be compared to the role of the magnitude of eigenvalues in continuously differential dynamical systems. Our results will help to understand the mechanism of such dangerous border collision bifurcations.

A Three-Species Food Chain System with Two Types of Functional Responses

Do, Younghae,Baek, Hunki,Lim, Yongdo,Lim, Dongkyu Hindawi Publishing Corporation 2011 Abstract and applied analysis Vol.2011 No.-

<P>In recent decades, many researchers have investigated the ecological models with three and more species to understand complex dynamical behaviors of ecological systems in nature. However, when they studied the models with three species, they have just considered the functional responses between prey and mid-predator and between mid-predator and top predator as the same type. However, in the paper, in order to describe more realistic ecological world, a three-species food chain system with two types of functional response, Holling type and Beddington-DeAngelis type, is considered. It is shown that this system is dissipative. Also, the local and global stability of equilibrium points of the system is established. In addition, conditions for the persistence of the system are found according to the existence of limit cycles. Some numerical examples are given to substantiate our theoretical results. Moreover, we provide numerical evidence of the existence of chaotic phenomena by illustrating bifurcation diagrams of system and by calculating the largest Lyapunov exponent.</P>

Dangerous border-collision bifurcations

Younghae Do,Sang Dong Kim,Philsu Kim,Hun Ki Baek 한국산업응용수학회 2006 한국산업응용수학회 학술대회 논문집 Vol.1 No.1

In this talk, we show our current results for dangerous border collision bifurcation characterized by exhibiting a stable fixed point before and after the critical bifurcation point, but the unbounded behavior of orbits at the critical bifurcation point. Dangerous bifurcations reveal a matter of serious concern for practical systems modeled by piecewise smooth maps, because there is no way of giving any signal of the impending collapse or unboundedness. Through the talk, we introduce the mechanism causing the occurrence of such bifurcations. Based on this mechanism, we find the qualitative type of the fixed point at the critical bifurcation value and show nonsmooth invariant manifolds of such fixed point, which can not be seen in linear systems.

Optimal harmonic response in a confined Bödewadt boundary layer flow.

Do, Younghae,Lopez, Juan M,Marques, Francisco Published by the American Physical Society through 2010 Physical review. E, Statistical, nonlinear, and so Vol.82 No.3

<P>The Bödewadt boundary layer flow on the stationary bottom end wall of a finite rotating cylinder is very sensitive to perturbations and noise. Axisymmetric radial waves propagating inward have been observed experimentally and numerically before the appearance of spiral three-dimensional instabilities. In this study, the sensitivity and response of the finite Bödewadt flow to a harmonic modulation of the rotation rate are analyzed. A comprehensive exploration of response to variations in the amplitude and frequency of the forcing has been carried out. There are sharply delineated linear- and nonlinear-response regimes, with a sharp transition between them at moderate amplitudes. The periodic forcing leads to a steady-streaming flow, even in the linear-response regime, and to a period-doubling bifurcation in the nonlinear regime. Frequency response curves at different forcing amplitudes over a wide range of frequencies have been computed and used to identify the frequency band that excites the axisymmetric radial waves and the forcing frequency that elicits the strongest response. Finally, we have shown that the axisymmetric waves always decay to the steady basic state when the harmonic modulation is suppressed, and conclude that the experimentally observed persistent circular waves are not self-sustained.</P>

Crop phenomics to genomics in the mathematical point of view

Younghae Do 한국육종학회 2023 한국육종학회 공동학술발표집 Vol.2023 No.-

On Semi-weakly n-Hyponormal Weighted Shifts

Do, Younghae,Exner, George,Jung, Il Bong,Li, Chunji Springer-Verlag 2012 Integral equations and operator theory Vol.73 No.1

Challenge to the top

Younghae Do 한국산업응용수학회 2009 한국산업응용수학회 학술대회 논문집 Vol.4 No.2

Fluid dynamics is one of the most challenging and exciting fields of scientific activity simply because of the complexity of the subject and the breadth of the applications. The quest for deeper understanding has inspired numerous advances in applied mathematics, computational physics, and experimental techniques. To create key growth-generating fields, it is necessary to develop the technique for analyzing fluid flows. Our research team, Computation and Methodology in Applied Fluid Dynamics, at Kyungpook National university focuses on the mathematical modeling for fluid systems, the development of problem-solving methodologies and robust tools for solution of fluid problems, and analysis of mathematical theories for phenomena observed in fluid dynamics.