环境干扰下分形生长的定方位控制

Directed control for fractal growth with environmental disturbance

中文关键词  环境干扰  分形生长  控制

英文关键词  environmental disturbance  fractal growth  control

中文摘要

      针对复杂无序的实际分形生长系统, 研究了环境干扰下分形生长的定方位控制模型. 不同于以往对分形生长的定方位的研究仅限于对它的实验方面的讨论, 本文利用范数理论得到了干扰项为广义函数时控制生长粒子凝聚到不同方位的定量方法. 利用所提出的控制方法解决了干扰项为更一般函数形式的定方向生长问题, 并以非线性项为二次多项式、正弦函数为例, 运用所得的定量关系对该系统不同作用区域的生长粒子进行了控制, 仿真结果表明了该控制方法的有效性.

英文摘要

      For a complex and disordered system of real fractal growth, the control model of the directed growth of the fractal growth with environmental disturbance is studied. Being different from the past studies on directed growth of the fractal growth based on their experiments, this work is concerned with the directed growth of the fractal growth theoretically. By the norm theory, we obtain a quantitative method for controlling the growing particles to aggregate in different regions when the environmental disturbance is a generalized function. The directed growth problem with the environmental disturbance in a more general functional form is solved by using the above obtained control method. Two examples of disturbances in quadratic polynomial and sinusoidal function are given, respectively. Simulation results illustrate that the growing particles will aggregate into the controlled regions when the corresponding controlled methods for associated growth regions are applied.