相邻两海域渔业资源模型的动力学分析

Dynamic Analysis of Fishery Resource Models in Two Adjacent Sea Areas

在考虑相邻海域相互作用的前提下,引入鱼类自然增长、人类捕捞等因素,建立相邻两海域的渔业资源模型。首先利用雅可比矩阵等相关理论知识分析了Nash均衡点及边界均衡点的稳定性,然后通过数值模拟讨论该模型的分岔行为及多稳态现象,最后利用分岔图、最大Lyapunov指数、吸引子和吸引盆等工具,深入讨论了相关参数对渔业资源存量的影响。研究结果揭示了相邻两海域的渔业资源之间复杂的相互作用关系,表明了当参数处于一定范围时,渔业资源才能保持稳定,才更有利于资源的可持续发展。

Under the premise of considering the interaction of two adjacent seas,factors such as natural growth of fish and human fishing are introduced to establish a fishery resource model in two adjacent seas.The stability of Nash equilibrium points and boundary equilibrium point is firstly analyzed by using relevant theoretical knowledge such as Jacobi matrix,and then the bifurcation behavior and multistability phenomenon of the model are discussed by numerical simulation,finally the influence of the relevant parameters on the stock of fishery resources is discussed in depth by using tools such as bifurcation diagrams,maximal Lyapunov exponents,attractors and attractor basins,and so on.The results of the study reveal the complex interactions between the fishery resources in the two adjacent seas,which can remain stable only when the parameters are in a certain range,which is conducive to the sustainable development of the resources.