| The management of the renew resources relates to keep on resources development, so it is important meaning in the economy and biology . According to experiments of the living creature, this thesis considers the influent factors of the cluster growth, establishes the parameter, builds up the system, and analysis it's qualitative; According to the theories, we can control the parameter, make the system balance Because of more complicated complexity of the model, the common mathematical methods can hardly handle that system, this text quotes from the strategy to learn the control theory method-- the biggest value of the system; After carrying on the qualitative analysis to the system, verify the conclusions to a numerical solid example, and really imitate for a sketch.This thesis takes the half open fishing ground for example, appling the differential calculus and the control knowledge, studies the prey-peyer system with II function, supposing the harvesting effort and growth densities be proportion, harvesting one; The government tax control the system, make it balance: When the harvesting effort quantity greatly, cause the group densities decrease, then the government increases the revenue from tax. When the harvesting effort quantity small, the group densities increment, the government reduces the revenue from tax, encouraging harvesting. we build up the harvesting model, get a superior succeed in harvesting with the revenue from tax strategy, provide the theories to the management of the fishing ground .In consideration of the ecology and economics meaning, the followings are all discussed on the district: Each sign represents the meaning as follows: x ( t ), y ( t ) mean the growth group densities; K ,L mean environments' biggest accept quantity densities respectively, r ,s mean the growth rates, d > 0 means the death rate of prey for food,β,α, m are normal numbers, mean the harvesting rate , the half saturated constant and the reservation rates respectively, E means that the unit succeeds in harvesting to work, q means the harvesting coefficient,τmeans the revenue tax that succeed in harvesting the unit living creature, p means the price of the unit, C means the harvesting cost. The beginning worth x ( 0 )> 0, y ( 0 )> 0.The model (1 - 1) researches the prey–preyer system with traditional II function:succeed in harvesting one( prey for food only having death rate) , get the equilibrium of the system; To the equilibrium point, with the stability theories, analy the equilibrium stability; With keeping on the biggest development into target, get the biggest value of the target function. The model (2 - 1) researches the prey-preyer system with Michaelis - Menten the ratio of function dependently:the method is the same with model (1 - 1) .The model (3 - 1)(4 - 1) , assumping that the harvesting effort quantity relate to the growth densities, constitute the motive system, matching the actual model: join the revenue from tax control in harvesting effort quantity, to keep the living creature balance, the economic target is to make social moment income biggest, the living creature target is to obstruct the fishes depopulation, the revenue from tax conduct and actions controls the tool, distinguishing the foundation in the (1 - 1)(2 - 1) , considering the economy and the price cost factor, build up the model: get the equilibrium of the system; To the equilibrium point, with the stability theories, analy the equilibrium stability; With keeping on the biggest development into target, get the biggest value of the target function. Apply the control theories, get a superior revenue from tax strategy.The model (5 - 1) on the foundation (4 - 1) , considers the model of two with inside growth rate respectively: model, apply in actual, give contented numerals of conditional stability analysis, really imitate to a sketch, verify the ex- literary style theory . |
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