Nonlinear Dynamic Analysis Of Three Types Of Fisheries Resource Models

In this paper, we build three type models of fishery resources from the perspective of economics and biology, focusing on researching the long-term evolution of fishery resources, and then explore the sustainable use of fishery resource.Above all, it has introduced the background and significance of this study, and described the current situation of the sustainable use of resources by foreign scholars and domestic scholars.Next, we build the following three type dynamic models by considering market prices,multi-generation co-existence and other factors.The first model: we consider the bounded rationality on fishing and suppose that adjusting intensity of market price in relate of the market demand and harvested, and then study the interaction of fish stock, harvest and market price; the second model: according to the needs of society for different stages of fishery resources, this paper is consider the bounded rationality fishing of the different stages fishery resource, and suppose market price is fixed value and resource is multi-generational co-existence; the third model: according to the different needs of society for fisheries resources, this paper is consider the bounded rationality fishing of the different stages fishery resource, and suppose market price is linear variable and resource is multi-generational co-existence.One after another, we give more comprehensive analysis of the equilibrium point of the existence and local stability of the models through theoretical analysis and numerical simulation.For researching the evolution of resource under different environmental conditions, we draw the time sequence diagram, phase diagram, one-dimensional bifurcation and two-dimensional bifurcation diagram of the systems by numerical simulation.Eventually, through graphical analysis of three models we have following conclusions: first, when the adjustment speed of fishing is accelerated according to the profit margins, or changes of market supply and demand is also quickly, the resources may maintain a stable reserve; second, the market price and fishing intensity of capture only the second generation resource can be slightly larger than capture only the first generations resource's in the complete market conditions; when capturing two generations resources, market price may relatively low and the relative intensity of fishin may be relatively big; third, when only capture the second generation fishery resources, the highest market price can be slightly larger than other situations in the un-complete market conditions; highest market price and the intensity of fishing played a significant impact in the market stability, then we can reasonable regulate its relationship for better maintain the market economic stability.