摘要
讨论了一类具避难所的次线性型食饵-捕食收获模型.应用Hurwize判据和Dulac判据分析了系统平衡点的局部和全局性态,通过Pioncare-Bendixson环域定理证明了极限环的存在唯一性,利用Pontyagin最大值原理得到了两种群的最优收获策略.最终发现避难所对此系统具有稳定化作用,且最优收获策略对生物资源的可持续利用具有一定实用价值.
A harvesting prey-predator model with shelter and sub linear functional response are discussed. By applying the Hurwize criterion and Dulac criterion, the local and global behavior of equilibrium points of the system are analyzed, through the Pioncare-Bendixson ring region theorem, the limit cycle existence and uniqueness are proved, and the optimal harvesting strategy is obtained by using the Pontyagin maximum principle. The stabilizing effect of prey refuge is obtained, and the optimal harvesting strategy provides a practical value for the sustainable use of biological resources.
出处
《北华大学学报（自然科学版）》
CAS
2016年第4期427-433,共7页
Journal of Beihua University（Natural Science）
基金
国家自然科学基金项目(U1504105)
河南省科技攻关计划项目(122102210060)
南阳市软科学研究计划项目(RKX06)
关键词
避难所
次线性
平衡点
极限环
最优收获
shelter
sub linear
equilibrium point
limit cycle
optimal harvesting
