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关于三维轨迹中的分形维数与相遇之间的关系。

On the relationship between fractal dimension and encounters in three-dimensional trajectories.

作者信息

Uttieri Marco, Cianelli Daniela, Strickler J Rudi, Zambianchi Enrico

机构信息

Department of Environmental Sciences, University of Naples "Parthenope", Via De Gasperi 5, 80133 Napoli, Italy.

出版信息

J Theor Biol. 2007 Aug 7;247(3):480-91. doi: 10.1016/j.jtbi.2007.03.026. Epub 2007 Mar 24.

DOI:10.1016/j.jtbi.2007.03.026
PMID:17467741
Abstract

The encounter of individuals-prey, predators and mates-living in the surrounding environment is a fundamental process in the life of an organism. Along with the sensory abilities, this process will be regulated by the movement rules adopted by the individual. In this work we discuss the encounter-enhancement effect due to different natatorial modes by calculating the number of encounters realised by differently convoluted trajectories in two homogeneous distributions of particles. Using numerically generated trajectories representative of specific swimming behaviour, we demonstrate that high values of three-dimensional fractal dimension D(3D)(>1.9) are beneficial only at high concentration, whereas at low concentration less tortuous tracks (D(3D) approximately 1.5) are almost equally efficient. In the light of our results it is possible to better understand the behavioural adaptations evolved by individuals to thrive in their environment.

摘要

个体与周围环境中的猎物、捕食者和配偶的相遇是生物体生命中的一个基本过程。除了感官能力外,这个过程还将由个体采用的运动规则来调节。在这项工作中,我们通过计算在两种均匀分布的粒子中不同卷积轨迹实现的相遇次数,来讨论不同游泳模式产生的相遇增强效应。使用代表特定游泳行为的数值生成轨迹,我们证明三维分形维数D(3D)(>1.9)的高值仅在高浓度时才有益,而在低浓度时,较不曲折的轨迹(D(3D)约为1.5)几乎同样有效。根据我们的结果,可以更好地理解个体为在其环境中茁壮成长而进化出的行为适应性。

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