國立臺南大學教師基本資料

基本資料
姓名 吳昌鴻
系所 應用數學系
職稱 副教授
校內分機 596
傳真
辦公室/研究室 C209-4
E-mail changhong@mail.nutn.edu.tw
網址 https://sites.google.com/site/homepagechanghongwu/
專長/研究領域 偏微分方程、動態系統
 

畢業學校國別主修學門學位修業期間
國立台灣師範大學中華民國數學系學士2000/9-2004/6
國立台灣師範大學中華民國數學系碩士2005/9-2007/6
國立台灣師範大學中華民國數學系博士2007/9-2010/6

服務機關部門 / 系所職稱服務期間
國立板橋高級中學 實習教師2004/8-2005/7
美國俄亥俄州立大學數學生物中心訪問學者2009/8-2010/6
國防部99-1義務役預官2010/8-2011/7
淡江大學數學系博士後研究2011/8-2012/7
交通大學應用數學系博士後研究2012/8-2013/1

著作
名稱(with Jong-Shenq Guo) Existence and uniqueness of traveling waves for a monostable 2D lattice dynamical system
年度2008
類別期刊論文
摘要We study traveling waves for a two-dimensional lattice dynamical system with monostable nonlinearity. We prove that there is a minimal speed such that a traveling wave exists if and only if its speed is above this minimal speed. Then we show the uniqueness (up to translations) of wave profile for each given speed. Moreover, any wave profile is strictly monotone.
關鍵字Lattice dynamical system, monostable, traveling wave, wave speed, wave profile.
名稱(with Jong-Shenq Guo) Front propagation for a two dimensional periodic monostable lattice dynamical system
年度2010
類別期刊論文
摘要We study the traveling wave front solutions for a two-dimensional periodic lattice dynamical system with monostable nonlinearity. We first show that there is a minimal speed such that a traveling wave solution exists if and only if its speed is above this minimal speed. Then we prove that any wave profile is strictly monotone. Finally, we derive the convergence of discretized minimal speed to the continuous minimal speed.
關鍵字Lattice dynamical system, monostable, traveling wave, wave speed, wave profile.
名稱(with Jong-Shenq Guo) Entire solutions for a two-componentcompetition system in a lattice
年度2010
類別期刊論文
摘要We study entire solutions of a two-component competition system with Lotka-Volterra type nonlinearity in a lattice. It is known that this system has traveling wave front solutions and enjoys comparison principle. Based on these solutions, we construct some new entire solutions which behave as two traveling wave fronts moving towards each other from both sides of x-axis.
關鍵字Lattice dynamical system, entire solution, traveling wave front, wave speed
名稱(with Jong-Shenq Guo) Wave propagation for a two-component lattice dynamical system arising in strong competition models
年度2011
類別期刊論文
摘要We study a Lokta-Volterra type competition system with bistable nonlinearity in which the habitat is divided into discrete niches. We show that there exist non-monotone stationary solutions when the migration coefficients are sufficiently small. Also, we prove that the propagation failure phenomenon occurs. Finally, we focus on the traveling wave with nonzero wave speed. By investigating the asymptotic behavior of tails of wave profiles, we show that nonzero speed wave profiles are monotone. Moreover, the nonzero wave speed is unique in the sense that the wave cannot propagate with two different nonzero wave speeds.
關鍵字Lattice dynamical system, stationary solution, propagation failure, traveling wave, wave speed.
名稱(with Yuan Lou) Global dynamics of atritrophic model for twopatches with cost of dispersal
年度2011
類別期刊論文
摘要To understand how cost of dispersal affects population dynamics, we study a three-trophic level food chain model, proposed by DeAngelis et al. \cite{DL}, in two patches. The system consists of one resource species, two consumers and a top predator. The top predator feeds on two consumers and both consumers feed on the resource. Only consumers move between the patches, possibly with a fraction of loss in population during the movement. The two competing consumers are identical in every aspect except their dispersal rates between two patches. If two consumers have the same dispersal rate from patch 1 to patch 2, we completely determine the global dynamics of the model and show that there exists an ``optimal" dispersal rate from patch 2 to patch 1 for the consumer such that, in terms of the theory of Adaptive Dynamics, it is a globally evolutionarily stable strategy and also a convergent stable strategy. If there is a minimum dispersal speed from patch 1 to patch 2, we are able to completely determine the evolutionarily stable strategy for dispersal between two patches. Our results offer insights into the evolution of dispersal in muiti-trophic level food chains, e.g., how the evolution of fast or slow dispersal for the consumer species depend upon the variation of the predation risk in the habitat. Our result suggests that even if most individuals die during the movement, a positive dispersal rate can still evolve.
關鍵字Dispersal, patch dynamics, food chain, cost of dispersal, optimal dispersal strategy
名稱(with Jong-Shenq Guo) Traveling wave front fora two-component latticedynamical system arisingin competition models
年度2012
類別期刊論文
摘要We study traveling front solutions for a two-component system on a one-dimensional lattice. This system arises in the study of the competition between two species with diffusion (or migration), if we divide the habitat into discrete regions or niches. We consider the case when the nonlinear source terms are of Lotka–Volterra type and of monostable case. We first show that there is a positive constant (the minimal wave speed) such that a traveling front exists if and only if its speed is above this minimal wave speed. Then we show that any wave profile is strictly monotone. Moreover, under some conditions, we show that the wave profile is unique (up to translations) for a given wave speed. Finally, we characterize the minimal wave speed by the parameters in the system.
關鍵字Traveling front, Lattice dynamical system, Competition model, Monostable, Minimal wave speed, Wave profile
名稱(with Jong-Shenq Guo) Recent developments onwave propagation in 2-species competitionsystems
年度2012
類別期刊論文
摘要In this paper, we shall survey some recent results on the wave propagation in 2-species competition systems with Lotka-Volterra type nonlinearity. This includes systems with continuous and discrete diffusion (or migration). We are interested in both monostable case and bistable with strong competition case. Questions on minimal speed for the monostable case, uniqueness of wave speed and propagation failure in the bistable case, monotonicity and uniqueness of wave profile for both cases are addressed. Finally, we give some open problems on wave propagation in 2-species competition systems.
關鍵字Lattice dynamical system, traveling wavefront, bistable, monostable, wave speed.
名稱(with Jong-Shenq Guo) On a free boundary problem for atwo-species weak competition system
年度2012
類別期刊論文
摘要We study a Lotka-Volterra type weak competition model with a free boundary in a one-dimensional habitat. The main objective is to understand the asymptotic behavior of two competing species spreading via a free boundary. We also provide some sufficient conditions for spreading success and spreading failure, respectively. Finally, when spreading successfully, we provide an estimate to show that the spreading speed (if exists) cannot be faster than the minimal speed of traveling wavefront solutions for the competition model on the whole real line without a free boundary.
關鍵字Lotka-Volterra model, free boundary, spreading-vanishing dichotomy, spreading speed
名稱Spreading speed and traveling waves for a two-species weak competition system with free boundary
年度2013
類別期刊論文
摘要In this paper, we will focus on the spreading speed for a Lotka-Volterra type weak competition model with free boundary in one-dimensional habitat. Based on the comparison principle for free boundary problems, we provide some estimates of the spreading speed. Also, we deal with traveling wave solutions for the same model and show that there exists a traveling wave solution with monotone profile using a shooting method and the Schauders fixed point theorem.
關鍵字Lotka-Volterra model, Free boundary, Spreading speed, Traveling wave, Wave speed
名稱(with Jong-Shenq Guo) Dynamics for a two-species competition-diffusion model with two free boundaries
年度2015
類別期刊論文
摘要To understand the spreading and interaction of two-competing species, we study the dynamics for a two-species competition–diffusion model with two free boundaries. Here, the two free boundaries which describe the spreading fronts of two competing species, respectively, may intersect each other. Our result shows there exists a critical value such that the superior competitor always spreads successfully if its territory size is above this constant at some time. Otherwise, the superior competitor can be wiped out by the inferior competitor. Moreover, if the inferior competitor does not spread fast enough such that the superior competitor can catch up with it, the inferior competitor will be wiped out eventually and then a spreading–vanishing trichotomy is established. We also provide some characterization of the spreading–vanishing trichotomy via some parameters of the model. On the other hand, when the superior competitor spreads successfully but with a sufficiently low speed, the inferior competitor can also spread successfully even the superior species is much stronger than the weaker one. It means that the inferior competitor can survive if the superior species cannot catch up with it.
關鍵字competition–diffusion model, free boundary problem, spreading– vanishing trichotomy, population dynamics
名稱The minimal habitat size for spreading in a weak competition system with two free boundaries
年度2015
類別期刊論文
摘要In this paper, we focus on the dynamics for a Lotka–Volterra type weak competition system with two free boundaries, where free boundaries which may intersect each other as time evolves are used to describe the spreading of two competing species, respectively. In the weak competition case, the dynamics of this model can be classified into four cases, which forms a spreading–vanishing quartering. The notion of the minimal habitat size for spreading is introduced to determine if species can always spread. Some sufficient conditions for spreading and vanishing are established. Also, when spreading occurs, some rough estimates for spreading speed and the long-time behavior of solutions are established
關鍵字Competition–diffusion model; Free boundary problem; Spreading–vanishing quartering; The minimal habitat size
名稱(with Jong-Shenq Guo, Yi Wang and Chin-Chin Wu) The minimal speed of traveling wave solutions for a diffusive three species competition system
年度2015
類別期刊論文
摘要In this paper, we study the minimal speed of traveling wave solutions for a diffusive three species competition system. Our main concern is the linear determinacy for the minimal speed. We provide some conditions on the parameters of the competition system such that the linear determinacy is assured. The main idea is by studying the linear determinacy of the corresponding approximated lattice dynamical systems and using the discrete Fourier transform.
關鍵字Three species competition system, Lattice dynamical system, Traveling wave, Minimal speed, Linear determinacy
名稱(with Jong-Shenq Guo, Hiroshi Matano and Masahiko Shimojo) On a free boundary problem for the curvature flow with driving force
年度2016
類別期刊論文
摘要We study a free boundary problem associated with the curvature dependent motion of planar curves in the upper half plane whose two endpoints slide along the horizontal axis with prescribed fixed contact angles. Our first main result concerns the classification of solutions; every solution falls into one of the three categories, namely, area expanding, area bounded and area shrinking types. We then study in detail the asymptotic behavior of solutions in each category. Among other things we show that solutions are asymptotically self-similar both in the area expanding and the area shrinking cases, while solutions converge to either a stationary solution or a traveling wave in the area bounded case. We also prove results on the concavity properties of solutions. One of the main tools of this paper is the intersection number principle, however in order to deal with solutions with free boundaries, we introduce what we call “the extended intersection number principle”, which turns out to be exceedingly useful in handling curves with moving endpoints.
關鍵字curvature flow, free boundary problem, motion of planar curves, asymptotically self-similar, convergence, isoperimetric ratio, singularity, extended intersection number principle
名稱The optimal dispersal strategy: a two-patch model with travel loss
年度2016
類別期刊論文
摘要The dispersal of organisms plays an important role in determining the dynamics of ecological models. Ecologically, it is of interest in understanding how dispersal strategy influences the distribution of populations. An ideal free distribution (IFD) of populations has been used to predict the distribution of organisms among patches, where a key assumption is to assume that species can move freely between patches without paying any cost. If instead one assumes that there are losses when species moves from one patch to another, then ideal free distributions may not appear. In this note, we examine a two-patch resident-mutant model with travel loss and predict the optimal dispersal strategy for resident and mutant. Moreover, such strategy which produces a non-IFD is evolutionarily stable. Some same and different features of patch models with travel loss are discussed.
關鍵字 Optimal dispersal strategy, patch model, travel loss, ideal free distribution
名稱A general approach to the asymptotic behavior of traveling waves in a class of three-component lattice dynamical systems
年度2016
類別期刊論文
摘要In this paper, we develop a general approach to deal with the asymptotic behavior of traveling wave solutions in a class of three-component lattice dynamical systems. Then we demonstrate an application of these results to construct entire solutions which behave as two traveling wave fronts moving towards each other from both sides of x-axis for a three-species competition system with Lotka–Volterra type nonlinearity in a lattice.
關鍵字Lattice dynamical systems, Traveling wave solutions, Asymptotic behavior, Entire solution, Lotka–Volterra model
名稱(with Chiu-Yen Kao, Chih-Wen Shih) Absolute stability and synchronization in neural field models with transmission delays
年度2016
類別期刊論文
摘要Neural fields model macroscopic parts of the cortex which involve several populations of neurons. We consider a class of neural field models which are represented by integro-differential equations with transmission time delays which are space-dependent. The considered domains underlying the systems can be bounded or unbounded. A new approach, called sequential contracting, instead of the conventional Lyapunov functional technique, is employed to investigate the global dynamics of such systems. Sufficient conditions for the absolute stability and synchronization of the systems are established. Several numerical examples are presented to demonstrate the theoretical results.
關鍵字Absolute stability, Synchronization, Neural field models, Delay equations
名稱(with Harunori Monobe) On a free boundary problem for a reaction-diffusion-advection logistic model in heterogeneous environment,
年度2016
類別期刊論文
摘要In this paper, we investigate a reaction–diffusion–advection equation with a free boundary which models the spreading of an invasive species in one-dimensional heterogeneous environments. We assume that the species has a tendency to move upward along the resource gradient in addition to random dispersal, and the spreading mechanism of species is determined by a Stefan-type condition. Investigating the sign of the principal eigenvalue of the associated linearized eigenvalue problem, under certain conditions we obtain the sharp criteria for spreading and vanishing via system parameters. Also, we establish the long-time behavior of the solution and the asymptotic spreading speed. Finally, some biological implications are discussed.
關鍵字Free boundary problem; Reaction–diffusion–advection equation; Heterogeneous environments; Population dynamics
名稱(with Hirokazu Ninomiya)Traveling curved waves in two dimensional excitable media
年度2017
類別期刊論文
摘要This paper treats a free boundary problem in two-dimensional excitable media arising from a singular limiting problem of a FitzHughNagumo-type reaction-diffusion system. The existence and uniqueness up to translations of two-dimensional traveling curved waves solutions is shown. To study the stability of the waves, the local and global existence and uniqueness of solutions to the free boundary problem near the waves under certain assumptions is established. The notion of the arrival time is introduced to estimate the propagation speed of solutions to the free boundary problem, which allows us to establish the asymptotic stability of traveling curved waves by using the comparison principle. It is also pointed out that the gradient blowup can take place if the initial data are far from the traveling curved waves, which means the interface may not always be represented by a graph.
關鍵字traveling curved waves, V-shaped traveling waves, front, back, excitable media
名稱(with Yin-Liang Huang) Positive steady states of reaction-diffusion-advection competition models in periodic environment
年度2017
類別期刊論文
摘要In this paper, we consider the positive steady states for reaction–diffusion–advection competition models in the whole space with a spatially periodic structure. Under the spatially periodic setting, we establish sufficient conditions for the existence of positive steady states of this model, respectively, by investigating the sign of the principal eigenvalue for some linearized eigenvalue problems. As an application, a Lotka–Volterra reaction–diffusion–advection model for two competing species in a spatially periodic environment is considered. Finally, some numerical simulations are presented to seek dynamical behaviors.
關鍵字Positive steady states, Reaction–diffusion–advection, Population dynamics, Periodic environment