具有时滞的游荡蜘蛛模型的分支分析  

Bifurcation analysis for a delayed wandered spiders model

作　　者：袁合才[1] 李培峦[2] 

机构地区：[1]华北水利水电大学数学与信息科学学院,郑州450045 [2]河南科技大学数学与统计学院,洛阳471023

出　　处：《黑龙江大学自然科学学报》2015年第3期302-311,共10页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11101126);河南省科技厅2011年基础与前沿技术研究计划项目(112300410040)

摘　　要：研究一类具有时滞的游荡蜘蛛模型,选择时滞τ为分支参数,当时滞τ通过一系列的临界值时,Hopf分支产生,即当时滞τ通过某些临界值时,从平衡点处产生一簇周期解。运用中心流型定理和规范型理论,研究分支周期解的特性,包括Hopf分支的稳定性、分支方向、周期。数值模拟验证了结论的正确性,补充了已有的结果。A delayed wandered spider model is investigated. By choosing the delay r as a bifurcation parameter, it is shown that Hopf bifurcation can occur when τ passes a sequence of critical values. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. Applying the center manifold theory and normal form theorem, the nature of bifurcation periodic solutions （for example, the stability, the solution ets. ） is investigated. Some numerical simulations direction and the periodic of Hopf bifurcation are given to justify the theoretical analysis resuits. The results complement previously known results.

关 键 词：捕食-被捕食 HOPF分支 稳定性 游荡蜘蛛 

分 类 号：O175.13[理学—数学]