一类时空离散捕食系统的混沌与斑图转变

Chaos and pattern transformation of a spatiotemporal discrete predator-prey system

探讨了一类时空离散Leslie-Gower型捕食系统的复杂时空动力学行为.运用分岔定理分析了该系统在不动点附近发生倍周期分岔、Neimark-Sacker分岔和图灵分岔的条件.通过分岔图和最大李雅普诺夫指数展示了系统的分岔过程,借助空间振幅和时空发展的变化揭示了由分岔引发混沌路径上的斑图转变规律.结果表明:在倍周期分岔引发的混沌路径上,斑图呈现类似的周期加倍级联过程,系统经历了从冻结混沌到缺陷湍流的变化;在Neimark-Sacker分岔引发的混沌路径上,斑图以环状和螺旋波状为主,在周期和拟周期吸引子上经图灵失稳形成的斑图仍会呈现有序的时空带状结构,在混沌吸引子上形成的斑图虽然呈现无序的空间振幅变化,但在时空发展变化中会呈现某种整体有序局部混乱的湍流状态.

The complex spatiotemporal dynamics of a kind of spatiotemporal discrete Leslie-Gower type predator-prey system is discussed.The bifurcation theorem is used to analyze the conditions under which the system undergoes flip bifurcation,Neimark-Sacker bifurcation and Turing bifurcation near the immobility point.The bifurcation process of the system is demonstrated by the bifurcation diagram and the maximum Lyapunov exponent,the pattern transition on the route chaos triggered by the bifurcation is revealed by the changes of spatial amplitude and space-time development.The results show that the pattern indicate a similar period doubling cascade process on the route chaos caused by flip bifurcation,and the system goes through a change from frozen chaos to defect turbulence.The pattern is mainly shaped like annular and spiral waves on the route chaos caused by the Neimark-Sacker bifurcation,and the pattern formed by Turing instability on the periodic and quasi-periodic attractors displays the ordered spatial and temporal banded structure.The pattern formed on the chaotic attractor shows the spatial amplitude changes of disorder,however,some turbulence state with overall order and local chaos appears in the changes of space-time development diagram.