Bifurcations Analysis of Population invasion: on-Off intermittency and Basin Riddling
Bifurcations Analysis of Population invasion: on-Off intermittency and Basin Riddling
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种群入侵的分叉分析：开关间歇性和盆地打水
DOI：
10.1142/s0218127400000281
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
R. Ferrière
中科院分区：
文献类型：
--
作者：
O. Feo;R. Ferrière
研究了一类时间离散动力系统在失稳不变子空间中存在吸引子时的局部分岔问题。该系统描述了两个物种在恒定环境中的竞争；不变子空间包含单种吸引子；吸引子在一个不变子空间中失去稳定性意味着相应的物种（即“常驻”物种）成为其竞争对手无法入侵的物种。全局动力学可以通过检查横向到不变子空间的李雅普诺夫指数的符号结构来理解。当横向Lyapunov指数（为自然测度计算）随着参数的变化从负变为正时，系统经历了所谓的井喷分岔。我们揭示了与爆裂分岔相关的两种一般情况：(1)涉及异斜混沌和开关间歇的co维-2分岔；(2)导致渐近不确定性的一系列谜语分岔。这两种情况的一个共同点是“常驻”种子空间包含多个不同时改变符号的横向Lyapunov指数的不变集合。这个简单的模型为研究井喷分岔结构提供了一个简短的典型系统列表。从生物学的观点来看，结果表明在恒定的环境中相互入侵既不是共存的必要条件，也不是充分条件。
We investigate the local bifurcations experienced by a time-discrete dynamical system from population biology when there is an attractor in an invariant subspace that loses stability. The system describes competition between two species in a constant environment; invariant subspaces contain single-species attractors; the loss of stability of the attractor in one invariant subspace means that the corresponding species (i.e. the "resident" species) becomes invadable by its competitor. The global dynamics may be understood by examining the sign structure of Lyapunov exponents transverse to the invariant subspace. When the transverse Lyapunov exponent (computed for the natural measure) changes from negative to positive on varying a parameter, the system experiences a so-called blowout bifurcation. We unfold two generic scenarios associated with blowout bifurcations: (1) a codimension-2 bifurcation involving heteroclinic chaos and on–off intermittency and (2) a sequence of riddling bifurcations that cause asymptotic indeterminacy. An ingredient that both scenarios have in common is the fact that the "resident" species subspace contains multiple invariant sets with transverse Lyapunov exponents that do not change sign simultaneously. This simple model adds on a short list of archetypical systems that are needed to investigate the structure of blowout bifurcations. From a biological viewpoint, the results imply that mutual invasibility in a constant environment is neither a necessary nor a sufficient condition for coexistence.