1、1生态环境系统中一类相互作用生态种群的动态优化与控制(英文)AbstractEcological environment system is a complex information system requiring the interdisciplinary employment of sciences of biology， environment， information， mathematics as well as the intensive study of computer science. The study of decision on macro optimistic c
2、ontrol of ecological system has in recent years become a major subject that mathematics and ecologists in and out of China explore in depth. Based on the needs of the current population ecology research to the development of macroscopic and microscopic， extending and the number of population ecology
3、 of complex system modeling， by discussing the analyticity and macro optimistic control of two kinds of interacting ecological population models with competitive mechanism and local stability， this paper makes more rigorous the control of ecological environment system and provides valuable methods f
4、or analytical analysis and control optimization of a kind of ecological system. It not only helps significantly with the modeling and analyzing of two kinds of competing and reciprocal ecological system， but also guides the analytical analysis and macro-control of more 2complex ecological environmen
5、t system. Key wordsEcological population model；Isocline equation；Density restraint；Analytical analysis；Optimization and control CLC numberO 175Document codeA The stability， bound and existence of limit cycle solution of the interactive kolmogorov model of two kinds of groups， namely， 2The Bound of t
6、he Kolmogorov Model The two-species competition and predator-prey model （1） F12 0 （The hunter gets the provision given by the bait） （3） When x2= 0， F11 0 which makes F1（0，K） = 0 （K is the hunters above critical density without the bait） （6） There is a constant number L 0 which makes 3F1（L，0） = 0 （L
7、is the bait loaded capacity without the hunter） （7） There is a constant number M 0 which makes F2（M，0） = 0 （M is the bait below critical density without the hunter） Finally， lets suppose that the hunters increasing only relies on the provision of the bait， then， Therefore， the trend that the integra
8、l curve in EN runs through is shown in Figure 3. 3The Existence of the Limit Cycle of the Kolmogorov Model In order to study the existence of the limit cycle of the kolmogorov model （1） ， lets suppose the following： （9） L M. （10） Through the isocline equation F1（x1，x2） = 0 of the prey， we can solve
9、that x2 is written as a function by x1 and the solution recorded as x2 = f（x1） is the only one， f is defined in the region 0，L and f is continuously differentiable and monotone decreasing， f（0） = K and f（L） = 0 exist. （11） The hunters isocline equation F2（x1，x2） = 0 can work out the only one x1 func
10、tion shown by x2marked x1= g（x2） ，the definition of g is in the region 0， and it is 4monotone increasing and continuously differentiable function， moreover， g（0） = M exists11. The above suppositions are the kolmogorov original conditions， but the following condition （9） presented by Rosenzwoig in 19
11、72 can be used to substitute them. （9） Suppose the isocline of the hunter and the prey can be shown in Figure 4， the point singularity plies at the rising part of the prey isocline. 4Prospect References 1 Zhang Jinyan. Geometric theory and branch problems of ordinary differential equations. Beijing：
12、 Peking University press， 1987： 125-160. 2 He Weilian. Permanence for single species model with feedback control andfinite continuous delays. Journal of Fuzhou University（Natural science Edition） ， 2009， 37（4）： 468-470. 3 Xiao Xiaonan. The establishment of decision model of the optimized information
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16、tive stochastic system. Journal of Xiamen University Natural Science， 2009， 48（2）： 170-173. 9 Dogru O， Duman O. Statistical approximation of Meyer-Konig and Zeller operators based on q-integers. Publ Math Debrecen， 2006， 68（1-2）：199-214. 10 Feng Chunbo， Fei Shumin. Nonlinear control systems 6analysis. 2nd ed， Beijing： Publishing House of Electronics Industry， 1998： 58-126. 11 Chen Lansun. Models and research methods of mathematical ecology. Beijing： Science Press， 1991： 105-196. 12 Gong Guanglu. Introduction of stochastic differential equations. Beijing： Peking University Press， 1995： 396-432
