Bifurcation Analysis Of Discrete Dynamical Model For Two Special Fishery Resource Zones

The overfishing of marine resource leads inexorably to the extinction of fish stocks,in order to control this situation,it is important to have a good knowledge of the global evolution of the resource and of the activity related to its exploitation.Especially in two different spatial zones connected by migrations,fish always swim in it back and forth,the fishery management authorities must deal with the possible fishery conflicts resulting for instance from the simultaneous exploitation of two fishing zones.In this paper,a specific stock-effort dynamic model is studied and it has great value to give analysis suggestions from the perspective of fishery management.In Chap 1,we describe the present situation of fishery resource management at home and abroad,the research content,research method and the organization of this paper are briefly given so that we have a first impression on this paper.In Chap 2,for the specific stock-effort dynamic model,we determine the existence and local stability of the nonnegative fixed points,the stability condition and sufficient condition for local bifurcations such as flip and Neimark-Sacker are determined by Jury condition and local bifurcation theorem.In Chap 3 and Chap 4,we determine the stability of positive fixed point at flip and Neimark-Sacker bifurcations with center manifold and normal forms respectively,and get the critical stability condition for those bifurcations on positive fixed point.In Chap 5,numerical simulations are displayed by MATLAB software to describe local bifurcations of positive fixed point and verify the results above.In the last Chap,a control function is introduced as the proportion of the revenue to be invested,for each fleet.By the artificial control of the system,the desired fixed point will arise and the important fluctuations are avoided in fishery system.