Optimal Harvest Model For Single Species Grouped By Years

Reproducible resources mean they can reproduce themselves in a natural way. But whether they can be utilized in a sustainable way depends on human beings reasonable behavior. We can't develop them above the threshold of natural reproduce, which means we should depend on scientific, policy and law to control the develop degree. We can only develop them in a sustainable way by protecting and controlling in a scientific way. How to calculate and control the degree not only depends on the knowledge of biology and economics, also depends on all scientific ways including mathematical and computer programming ways which do a great work in this paper.To explore the biologic resource of a single species grouped by ages, we construct a mathematic model to describe the dynamic behavior of this kind of biologic system. We focus on the discussion of the human beings' influence to the Anchovy's stable condition .So we know how to control it to get the optimal sustainable harvest and then we can provide reasonable management strategy in a scientific way.Based on the theories of Matrix disturbance and eigenvalue estimation, we discuss the stability of a nonlinear dynamic system. Also we get the c value to reach the optimal sustainable harvest.The main content is provided as follows:In chapter 1, we construct a mathematic model to describe the dynamic system for single species grouped by years after introduction of the related background.In chapter 2, we get the different stable yield on different c value by programming Visual Basic.In chapter 3, we apply the model to guide fishery harvest strategy.In chapter 4, we try to explain the following three questions in a way combined with theoretic proof and Matlab programming.1.When a parameter c ( 0≤c≤30) is given, why the difference equations converges and the convergence has nothing to do with the initial fish population?2.Is it significant to test the stability depending on the perturbed equilibrium? To answer this question, we explore the robustness of this nonlinear dynamic system.3. The curve drawn by programming shows the simple monotonic relationship between the parameter c and the fish yield: increases first. It's necessary to discuss the monotony.