| speaker | type | title |
| Bendong Lou | Invited speaker | Influence of boundary conditions on the qualitative property of a reaction diffusion equation |
| abstract: Lou-Abstract.tex | ||
| Cantrell, Robert Stephen | Invited speaker | Avoidance behavior in intraguild predation communities: A cross diffusion model |
| abstract: A cross-diff usion model of an intraguild predation community where the intraguild prey employs a fi tness based avoidance strategy is examined. The avoidance strategy employed is to increase motility in response to negative local fi tness. Global existence of trajectories and the existence of a compact global attractor is proved. It is shown that if the intraguild prey has positive fi tness at any point in the habitat when trying to invade, then it will be uniformly persistent in the system if its avoidance tendency is sufficiently strong. This type of movement strategy can lead to coexistence states where the intraguild prey is marginalized to areas with low resource productivity while the intraguild predator maintains high densities in regions with abundant resources, a pattern observed in many real world intraguild predation systems. Additionally, the eff ects of fi tness based avoidance on eigenvalues in more general systems are discussed. This work is joint with Daniel Ryan. | ||
| Chung, Jaywan | Invited speaker | Introduction to Adaptive Dynamics for Ecology |
| abstract: | ||
| Do, Younghae | Invited speaker | Persistent coexistence of cyclically competing species in spatially extended ecosystems |
| abstract: A fundamental result in the evolutionary-game paradigm of cyclic competition in spatially extended ecological systems, as represented by the classic Reichenbach-Mobilia-Frey (RMF) model, is that high mobility tends to hamper or even exclude species coexistence. This result was obtained under the hypothesis that individuals move randomly without taking into account the suitability of their local environment. We incorporate local habitat suitability into the RMF model and investigate its effect on coexistence. In particular, we hypothesize the use of “basic instinct” of an individual to determine its movement at any time step. That is, an individual is more likely to move when the local habitat becomes hostile and is no longer favorable for survival and growth. We show that, when such local habitat suitability is taken into account, robust coexistence can emerge even in the high-mobility regime where extinction is certain in the RMF model. A surprising finding is that coexistence is accompanied by the occurrence of substantial empty space in the system. Reexamination of the RMF model confirms the necessity and the important role of empty space in coexistence. Our study implies that adaptation/movements according to local habitat suitability are a fundamental factor to promote species coexistence and, consequently, biodiversity. | ||
| Ei Shin-Ichiro | Invited speaker | Dynamics of Localized Solutions for Reaction-Diffusion Systems on Curved Surface |
| abstract: SurfaceCurveKAIST.pdf | ||
| Enatsu, Yoichi | Student speaker | Threshold dynamics for compartmental epidemic models with delays and related problems |
| abstract: abstract_yenatsu.pdf | ||
| Gani, Mohammad Osman | Student speaker | Alternans and Spiral Breakup in a Modified FitzHugh-Nagumo Model of Cardiac Cell Dynamics |
| abstract: Abstract_M. Osman Gani.pdf | ||
| He, Xiaoqing | Invited speaker | Global dynamics of the two-species Lotka-Volterra competition-diffusion system |
| abstract: In this talk, we investigate the combined effects of diffusion, spatial variation and competition ability on the global dynamics of a classical Lotka-Volterra competition-diffusion system. We establish the main results which determine the global asymptotic stability of semi-trivial as well as co-existence steady states. Hence a complete understanding of the change in dynamics is obtained immediately. | ||
| Hwang, Hyung Ju | Invited speaker | A mathematical model of T helper cell differentiation |
| abstract: Asthma is a complex chronic disease mainly characterized by inflammatory disorder of the airway and airway hyperresponsiveness (AHR). Its major symptoms include coughing, wheezing, breathlessness, and chest tightness. T helper cells play an important role in the immune system. Understanding T helper cell differentiation is a major interest in immune disorders such as asthma. Here we develop a mathematical model that is able to explain T helper cell differentiation. We simplify the complex network of the interactions between T helper cells and regulatory molecules by a mathematical model, a system of ordinary or partial differential equations. The model describes the nonlinear interactions between T helper cells and regulatory molecules in response to high, intermediate, and low levels of lipopolysaccharide (LPS), and characterizes development of different T helper cell phenotypes. Our results illustrate the mono-, bi-, and oneway-switches in the key regulatory parameter sets. The model also predicts coexistence of those phenotypes in a spatial domain under certain conditions. | ||
| Ijioma Ekeoma | Student speaker | Kinetic and Material Property Effects on fingering Instability in Counterflow Smoldering Combustion |
| abstract: IjiomaER_RDEConf.pdf | ||
| Ikeda, Hideo | Invited speaker | Dynamics of front solutions in heterogeneous diffusive media |
| abstract: We consider two component reaction-diffusion systems with a specific bistable and odd symmetric nonlinearity, which have the bifurcation structure of pitch-fork type of traveling front solutions with opposite velocities. Under this situation, we introduce a special heterogeneity, for example Heaviside-like abrupt change at the origin in the space, into diffusion coefficients. Numerically, the responses of traveling fronts via the heterogeneity can be classified into three types depending on the velocity of a traveling front and the height of the jump: passage, stoppage and reflection. The aim of this talk is to show the mathematical mechanism producing the three types of responses by reducing the PDE dynamics to a finite dimensional ODE system. | ||
| IKEDA, KOTA | Invited speaker | Collective motions of particles with diffusive interactions |
| abstract: ikeda_abstract_Daejeon.pdf | ||
| Kan-on, Yukio | Invited speaker | Structure on the set of radially symmetric positive stationary solutions for a competition-diffusion system |
| abstract: In this talk, we consider a reaction-diffusion system with density-dependent diffusion, which describes the dynamics of population density for a two competing species community, and discuss the structure on the set of radially symmetric positive stationary solutions for the system by assuming the habitat of the community to be a ball. To do this, we shall treat the diffusion rate, the interspecific competition rate and the dimension of the habitat as main bifurcation parameters, and employ the comparison principle and the implicit function theorem. | ||
| Kang,Kyungkeun | Invited speaker | A 2D-Model of Cell Sorting Induced by Propagation of Chemical Signals Along Spiral Waves |
| abstract: We study a model for cell sorting based in the presence of differential chemotactic sensitivities. The chemical waves which are responsible for the cell motion propagate along some spiral waves. We prove rigorously that cells with larger chemotactic sensitivity are trapped in a region close to the center of the spiral waves if these propagate along some archimedian spirals. | ||
| khhledze | Participant (Ph.D) | aArNZHbwkwZUXKdZC |
| abstract: USA | ||
| Kim, Yong-Jung | Invited speaker | Mathematical modeling of a random dispersal in heterogeneous environments |
| abstract: Abstract-YJKIM.pdf | ||
| Ko, Wonlyul | Invited speaker | Asymptotical behaviors of a general diffusive consumer-resource model with maturation delay |
| abstract: In this talk, we consider the asymptotic behavior of a diffusive delayed consumer-resource model with general functional response subject to homogeneous Neumann boundary conditions, where the discrete time delay covers the period from the birth of juvenile consumers to their maturity. We construct the threshold dynamics of their persistence and the extinction of the consumer. We also construct sufficient conditions for the global attractivity of the semitrivial and coexistence equilibria, and we study the Hopf bifurcations (stability switch: the existence of a branch with a bifurcated periodic solution) at these equilibria. Finally, we apply our results to consumer-resource models using Beddington-DeAngelis, Crowley-Martin, and ratio-dependent type functional responses. | ||
| Kuto, Kousuke | Invited speaker | Coexistence steady-states to the Lotka-Volterra competition model with diffusion and advection |
| abstract: Abstract-kuto.pdf | ||
| Kwon, Ohsang | Invited speaker | Evolution of dispersal toward fitness and starvation driven diffusion |
| abstract: 0Abstract-Kwon,Ohsang.pdf | ||
| Liang， Xing | Invited speaker | Spreading speeds and traveling waves of space-time periodic KPP equations with free boundary |
| abstract: In this talk, I will introduce our new results on the existence of spreading speed and traveling waves of space-time periodic KPP equations with free boundary | ||
| Lin,Zhigui | Invited speaker | Spreading fronts of the disease in an SIS epidemic model |
| abstract: This talk deals with a diffusive SIS epidemic model with a free boundary. We aim to use the dynamics of such a problem to understand the impact of spatial heterogeneity of environment on the persistence and extinction of an infectious disease. The free boundary is introduced to describe the transmission of the disease. The behaviors of positive solutions to a reaction-diffusion system in a radially symmetric domain are discussed. The basic reproduction number $R_0^D$ is defined for the reaction diffusion system with Dirichlet boundary condition, and then the basic reproduction number $R_0^F(t)$ is introduced for this spatial SIS model with the free boundary, sufficient conditions for the disease to vanish or spread are given. We prove that the disease will spread to the whole area if there exists a $t_0geq 0$ such that $R_{0}^F(t_0)geq 1$, while if $R_{0}^F(0)<1$, whether the disease is vanishing or spreading depends on the initial value of the infective. Our results show that the infectious disease in high-risk habitat is very dangerous, and early warning and effective control of the disease in low-risk habitat is necessary. | ||
| Lou, Yuan | Invited speaker | Evolution of Dispersal in Heterogeneous Environments: Finding ESS |
| abstract: From habitat degradation and climate change to spatial spread of invasive species, dispersal plays a central role in determining how organisms cope with a changing environment. How should organisms disperse optimally in heterogeneous environments? I will discuss some recent development on the evolution of dispersal, focusing on evolutionarily stable strategies (ESS) for dispersal. | ||
| Scotti, Tommaso | Student speaker | Does Toxicity Promote Coexistence? |
| abstract: Scotti_abstalk.pdf | ||
| Wei, Junjie | Invited speaker | On Hopf Bifurcation of Reaction-Diffusion Equations with Time Delay |
| abstract: | ||
| Yoon, Changwook | Student speaker | Bacterial chemotaxis without gradient-sensing |
| abstract: Models for chemotaxis are based on gradient sensing of individual organisms. The key contribution of Keller and Segel is showing that erratic movements of individuals may result in an accurate chemotaxis phenomenon as a group. In this talk we provide another option to understand chemotactic behavior when individuals do not sense the gradient of chemical concentration by any means. We show that, if individuals increase their motility to find food when they are hungry, an accurate chemotactic behavior is obtained without sensing the gradient. Such a random dispersal is called starvation driven diffusion. This model is surprisingly similar to the original derivation of Keller-Segel model. | ||