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Chaotic attractors in Atkinson-Allen model of four competing species.
Journal of Biological Dynamics ( IF 1.8 ) Pub Date : 2020-06-19 , DOI: 10.1080/17513758.2020.1779828
Mats Gyllenberg 1 , Jifa Jiang 2 , Lei Niu 3, 4
Affiliation  

We study the occurrence of chaos in the Atkinson–Allen model of four competing species, which plays the role as a discrete-time Lotka–Volterra-type model. We show that in this model chaos can be generated by a cascade of quasiperiod-doubling bifurcations starting from a supercritical Neimark–Sacker bifurcation of the unique positive fixed point. The chaotic attractor is contained in a globally attracting invariant manifold of codimension one, known as the carrying simplex. Biologically, our study implies that the invasion attempts by an invader into a trimorphic population under Atkinson–Allen dynamics can lead to chaos.



中文翻译:

Atkinson-Allen模型中四个竞争物种的混沌吸引子。

我们研究了四个竞争物种的Atkinson-Allen模型中混沌的发生,该模型起着离散时间Lotka-Volterra型模型的作用。我们表明,在该模型中,可以通过从唯一正定点的超临界Neimark-Sacker分叉开始的拟拟加倍分叉的级联生成混沌。混沌吸引子包含在一个整体吸引不变的二维维数中,称为携带单纯形。从生物学上讲,我们的研究表明,入侵者在阿特金森-艾伦动力学条件下入侵三态种群的企图会导致混乱。

更新日期:2020-06-19
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