Pioneer-Climax物种模型的动态分歧

Dynamic bifurcation of Pioneer-Climax species model

分歧是自然运动中的普遍现象,它所描述的是一个稳定的定态运动状态下当某种参数超过一个临界指标时就会跃迁到另一种运动状态。大自然中有很多分歧现象,如河水中突然出现一个漩涡、龙卷风的形成等。文章研究一类Pioneer-Climax物种模型的动态分歧问题,利用泛函中线性全连续场的谱理论、中心流形定理和吸引子分歧跃迁对Pioneer-Climax物种模型的动态分歧进行讨论,得到了分歧跃迁的参数临界值,给出了分歧解的表达式。

Bifurcation is a common phenomenon in natural motion,which describes a stable steady state of motion that jumps to another when a parameter exceeds a critical index.There are many diverging phenomena in nature,such as a sudden whirlpool in the river,the formation of tornadoes,and so on.In this paper,the dynamic bifurcation problem of a class of Pioneer-Climax species model is studied.The dynamic bifurcation of Pioneer-Climax species model is discussed by using the spectral theory of linear fully continuous field in functional,the central manifolds theorem and the bifurcation transition of attractor,and the critical value of the parameters of bifurcation transition is obtained.The expression of bifurcation solution is given.