http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
DYNAMICS OF A DISCRETE RATIO-DEPENDENT PREDATOR-PREY SYSTEM INCORPORATING HARVESTING
BAEK, HUNKI,HA, JUNSOO,HYUN, DAGYEONG,LEE, SANGMIN,PARK, SUNGJIN,SUH, JEONGWOOK The Youngnam Mathematical Society 2015 East Asian mathematical journal Vol.31 No.5
In this paper, we consider a discrete ratio-dependent predator-prey system with harvesting effect. In order to investigate dynamical behaviors of this system, first we find out all fixed points of the system and then classify their stabilities by using their Jacobian matrices and local stability method. Next, we display some numerical examples to substantiate theoretical results and finally, we show numerically, by means of a bifurcation diagram, that various dynamical behaviors including cycles, periodic doubling bifurcation and chaotic bands can be existed.
DYNAMICS OF AN IMPULSIVE FOOD CHAIN SYSTEM WITH A LOTKA-VOLTERRA FUNCTIONAL RESPONSE
HUNKI BAEK 한국산업응용수학회 2008 Journal of the Korean Society for Industrial and A Vol.12 No.3
We investigate a three species food chain system with Lotka-Volterra type functional response and impulsive perturbations. We find a condition for the local stability of prey or predator free periodic solutions by applying the Floquet theory and the comparison theorems and show the boundedness of this system. Furthermore, we illustrate some examples.
Bifurcation Analysis of a Spatiotemporal Parasite-host System
Baek, Hunki Department of Mathematics 2020 Kyungpook mathematical journal Vol.60 No.2
In this paper, we take into account a parasite-host system with reaction-diffusion. Firstly, we derive conditions for Hopf, Turing, and wave bifurcations of the system in the spatial domain by means of linear stability and bifurcation analysis. Secondly, we display numerical simulations in order to investigate Turing pattern formation. In fact, the numerical simulation discloses that typical Turing patterns, such as spotted, spot-stripelike mixtures and stripelike patterns, can be formed. In this study, we show that typical Turing patterns, which are well known in predator-prey systems ([7, 18, 25]), can be observed in a parasite-host system as well.
A HOLLING TYPE II FOOD CHAIN SYSTEM WITH BIOLOGICAL AND CHEMICAL CONTROLS
Baek, Hunki Korean Mathematical Society 2009 대한수학회논문집 Vol.24 No.2
For a class of Holling type II food chain systems with biological and chemical controls, we give conditions of the local stability of prey-free periodic solutions and of the permanence of the system. Further, we show the system is uniformly bounded.
On the Dynamical Behavior of a Two-Prey One-Predator System with Two-Type Functional Responses
Baek, Hunki Department of Mathematics 2013 Kyungpook mathematical journal Vol.53 No.4
In the paper, a two-prey one-predator system with defensive ability and Holling type-II functional responses is investigated. First, the stability of equilibrium points of the system is discussed and then conditions for the persistence of the system are established according to the existence of limit cycles. Numerical examples are illustrated to attest to our mathematical results. Finally, via bifurcation diagrams, various dynamic behaviors including chaotic phenomena are demonstrated.
Stability for a Holling Type IV Food Chain System With Impulsive Perturbations
Baek, Hunki,Do, Young-Hae Department of Mathematics 2008 Kyungpook mathematical journal Vol.48 No.3
We investigate a three species food chain system with a Holling type IV functional response and impulsive perturbations. We find conditions for local and global stabilities of prey(or predator) free periodic solutions by applying the Floquet theory and the comparison theorems.
Hunki BAEK,Younghae DO 한국산업응용수학회 2009 한국산업응용수학회 학술대회 논문집 Vol.2009 No.5
The dynamical relationships between predator and prey can be represented by the functional response which refers to the change in the density of prey attached per unit time per predator as the prey density changes. One of well-known functional responses is the Beddington-DeAngelis functional response introduced by Beddington [3] and DeAngelis et al [5], independently. The main difference of this functional response from a classical Holling type ones is that this one contains an extra term presenting mutual interference by predators. There are a lot of factors to be considered in the environment to describe more realistic relationships between predators and preys. One of important factors is seasonality, which is a kind of periodic fluctuation varying with changing seasons. Also, the seasonality has an effect on various parameters in the ecological systems. For this reason, it is valuable to carry out research on systems with periodic ecological parameters which might be quite naturally exposed such as those due to seasonal effects of weather or food supply etc [4,18]. There are several ways to reflect the effects caused by the seasonality on ecological systems [12,13,23]. In this paper we consider the intrinsic growth rate a of the prey population as periodically varying function of time due to seasonal variations. In other words we adopt a0 = a(1 + εsin(ωt)) as the intrinsic growth rate of the prey. Here the parameter ε represents the degree of seasonality, aε the magnitude of the perturbation in a0 and ω the angular frequency of the fluctuation caused by seasonality. Moreover, there are still some other factors that affect ecological system such as fire, flood, harvesting seasons etc, that are not suitable to be considered continually. These impulsive perturbations bring sudden change to the system. Such impulsive systems are found in almost every area of applied science and have been studied in many researches: impulsive birth [17,21], impulsive vaccination [6,19], chemotherapeutic treatment of disease [10,16]. In particular, the impulsively controlled prey-predator population systems have been investigated by a number of researchers [1,8,12?14,20,22,24?34]. Thus the field of research of impulsive differential equations with impulsive control terms seems to be a new growing interesting area in recent years. However, the two-prey and one-predator systems with seasonal effects and impulsive controls are less noticeable in spite of their importance. Now we develop the following new system with seasonality by bringing in a proportional periodic impulsive harvesting such as spraying pesticide for all species and a constant periodic releasing for the predator at different fixed moment. <<본문참조>> where x₁(t), x₂(t) and y(t) represent the population density of two preys and the predator at time t, respectively. The constant ai(i = 1, 2) are called the intrinsic growth rates of the prey population, bi(i = 1, 2) are the coefficients of intra-specific competition, ci(i = 1, 2) are the parameters representing competitive effects between two preys, ¾i(i = 1; 2) are the per-capita rates of the predation of the predator, di(i = 1, 2) and ei(i = 1, 2) are the half-saturation constants, the constant a₃ is the death rate of the predator, the terms μi(i = 1, 2) scale the impact of the predator interference, σi(i = 3; 4) are the rates of the conversing prey into the predator, λ and ω represent the magnitude and the frequency of the seasonal forcing terms, respectively, τ and T are the period of spaying pesticides(harvesting) and the impulsive immigration or the stock of the predator, respectively, 0 ≤ p₁, p₂, p₃ < 1 present the fraction of two preys and the predator which die due to harvesting or pesticides etc and q is the size of immigration or the stock of the predator. The main purpose of this paper is to investigate the condit
Baek, Hunki Department of Mathematics 2016 Kyungpook mathematical journal Vol.56 No.3
In this paper, we consider a discrete predator-prey system with Watt-type functional response and impulsive controls. First, we find sufficient conditions for stability of a prey-free positive periodic solution of the system by using the Floquet theory and then prove the boundedness of the system. In addition, a condition for the permanence of the system is also obtained. Finally, we illustrate some numerical examples to substantiate our theoretical results, and display bifurcation diagrams and trajectories of some solutions of the system via numerical simulations, which show that impulsive controls can give rise to various kinds of dynamic behaviors.