基于最大流原理的复杂生态系统分形结构

Fractal structures in complex ecosystems from maximum flux principle

生态系统具有分形等复杂性特点,一直是学术界关注的热点和难点.而现有的研究大都缺乏深入的动力学机理分析.针对这一空白,本文以一个远离平衡的复杂系统总是努力寻找一种优化过程,使得系统在给定的约束或代价下所获得的广义流最大这个思想出发,从微观动力学角度探讨了生态系统模式的分形长大过程.从尺度变化角度对分形生长思想进行了MATLAB数值模拟佐证.分析了影响分形维数的因素并比较了理论结果与实际例子,进而讨论了在实践中的可能应用.

Ecosystems are typically characteristic of fractals, complexity etc. , which remain elusive and controversial issues up to today. Recent research mainly lacks deep mechanism analysis. Focusing on this blank, this paper use the thought that a complex system far from equilibrium always trying to find an optimum process to gain maximized flux under a certain constraint or cost. We discussed the dynamical mechanisms of the fractal hierarchical growth in ecosystems. We revealed the mechanistic effects of many factors on the fractal dimension. We use MATLAB to simulate and further compared the theoretical analyses with the practical examples, and discusses the possible applications in the practice.