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Asymptotic behavior of solutions of a class of Ecological Mathematical Model

Author: ZhangLiJun
Tutor: ChenJuFang
School: Shaanxi Normal University
Course: Basic mathematics
Keywords: Continued survival Feedback control Stage structure Cannibalism Asymptotically stable
CLC: O175
Type: Master's thesis
Year: 2000
Downloads: 232
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Abstract

Humans and animals living in resource-limited settings, the long-term thriving. Competitive exclusion of animal populations and the law of the jungle, the consequences, why the balance of the ecology, fisheries catches carnivorous fish survival What impact so interesting biological problem of great concern by scholars of the mathematical community, through the establishment of a bio-mathematical model to describe and study the complex biological phenomena. Ecological environment, due to the competition between populations, inevitably produce the \Imagine an island, inhabited by foxes and hares, foxes eat rabbits, rabbit grazing. Grass is so rich, the rabbit No Worries without food, so blooms; over one rabbit, fox and easy to get food, Fox amount of easy growth, while the foxes increase in the number of eaten rabbit, fox group entered the hungry, the number dropped relatively safe, when the rabbit, so the bunny total number of pick-up, so the number of fox rabbit alternately increases and decreases, an endless cycle of gradually forming ecological homeostasis; great scientist Charles Darwin in his famous book \: \make populations facing extinction continued survival has an extremely important biological and practical significance. The stability of the positive equilibrium point and periodic solution is mathematical thinking accurate and scientific reflect on the persistent problem of biological populations, the continued survival of the population is actually a stability of the ecosystem. This article discussed the asymptotic nature of the ecosystem following three models: Model 1 is a functional response to X ^{1/2 predator - prey model x = x-α (t) x ^{3/2 -x ^{1/2 yy =-s (t) y β (t) x ^{1/2 y-ε (t) y ^{2 Here, x and y denote the prey and predator population density, a (t) ;/ J (t). (L), ...) is continuous and has a positive on the [0, + co), the lower bound of the cycle. > 0 in the periodic function. Model with feedback control side cycle SCllOlllf competition model: a I 11Z122 c11 [11 - all [Report of 11 Cong and a [) ilL and Jgi! the of l-Clllj Bian 0Itl1 one hundred Lll convex * called two = c cited work and the D-Factory 7 back Hang two hundred eleven 7 Yan Ding of ... Pakistan I1c] Pakistan [and a factory 10 TWINING Cong q! Cong) a bite bar plexus in2 BU ID whose coefficients are positive bounded function. Model 3 is the two-group competition model with stage structure: _ the uncle _ Ah Valley against the. . . _ r4 dollar. . / Sheep, _. A 7. . The hand _ Free back o_ / I. / More, I_'11 \\ __. The one Y _IJ___ \\ L_IO \\. U \\ f4. 2 (0 \\ *) T small) III 0, c; 100 B (two yi) 30, a D 0. This is called a and. . . *, Respectively. Juvenile and adult populations population density) variable, y () a 9 populations population density, and 0 = of-02 negative. Adult populations. Prey on juvenile handsome group of people and adult populations. And population. Competing. Been extensively studied in the two-dimensional competitive Lotka-Voltera system D, Po food prey system because of changes in the model coefficients symbols resulting research has become relatively complex. The experiments show that in some animal populations (especially low-grade animal plant predator predation functional response function has the form of a store. Literature stuffy model 1 when the coefficient is a constant of the situation made a qualitative study. Practice, however constant environment does not exist, the usual environmental factors change. functional reaction function must study in order to more accurately depict the ecosystem, time-varying environment Wan predator-prey system, especially the cycle coefficient model but because This model non-autonomy ecological model of autonomy model method in this powerless, which bring some difficulties to study the first part of this paper is to construct the final sector the domain and LyaPtmov function method to obtain a model populations continued survive a full set of conditions, as well as a system for the periodic system, periodic solution globally asymptotically stable and sufficient condition in the field of systems and control theory, the the biodynamic system control theory is an important branch of one of the populations in many research the continued survival of the literature on how to rescue the populations are threatened with extinction, its continued existence, generally there are two ways you can achieve by regulating natural populations, namely the so-called diffusion phenomena. alternative through artificial means , that we can find some of the control program (stocking and harvest) continued survival. Wen asked with feedback control *. Bu. - * Itn;. competitive system To be continued survival, achieved through the rational control to save the extinction of populations of the Day., little practicality Sol. * ler 1974 two strong group competing subsystems model of this paper is to study with feedback control SCllOlllY the asymptotic properties of the model in the text of N1 h1 population extinction into using the comparison theorem, B * wer fixed point theorem personal law, to obtain a set of sufficient conditions for the model stock sustainability, as well as systems for periodic system · periodic solution globally asymptotically stable and sufficient condition. reasonable control can save the extinction of the population, allowing the system to be continued survival. thus, in theory, provide extremely valuable to be endangered animal protection - Flash l feasibility of the program. stage structure model is a difficult but realistic significance of the work, the stage structure model studies Cannibalism is a novel issue. the students counseled environment, many populations the existence of Cannibalism phenomenon, the big fish eat \}}}}}

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