Analysis Of Common Fishery Resource Dynamical Model With Split Stream Competed By Two Players

In thi paper,we consider the mobility of fishery resources which are distributed withscale in two split streams of one river and harvested by two different fleet, take the sumof fishery stock as a system variable.We establish discrete dynamic model. We study thediscrete dynamic systems which are with and without the concern of predictive fishingseparately on the basis of singularities theory of irreversible mapping.Firstly, we assume that all the fishermen know complete information of fisherystock. We utilize two parties compete to reach the fishing volume dose at the Nashequilibrium, which is a nonlinear function involving a proportional distribution. We usenumerical analysis and simulate method analyze the existence of fixed points and thestability and local bifurcation of them, and discuss the global bifurcation of limitedattracting set and its attracting domain.Secondly, we supposing that all the fishermen know incomplete information offishery stock and just predict the fishery stock which suit for themselves. We establish atwo-dimensional mapping system on the basis of the previous one-dimensional system.While examining the local stability and bifurcation of fixed points using thenoninvertible map theory, it explores its global dynamics behavior. The sustainableutilization condition of resource is obtained by the structural change of the attractor andattracting domain of the system.