Fractal And Dynamic Characters Of Complex Ecosystem

Ecosystem is a complex non-linear system far from equilibrium. Its non-linear complexity comes from the reciprocity among the subsystems. Furthermore, it has chaotic characters indeed because of the multivariant of both subsystems and influencing factors. That is to say, ecosystem is sensitive to the initial conditions and has fractal characters. But there are still certain rules hidden in the mess. After years of study, researchers discover that ecosystems have the characters of hierarchy and heterogeneity. Although people have noticed these characters early, the studies keep rest on the phenomenal levels which are lack of deep-seated theoretical bases of physics and mathematics. Most studies of differential equation models in ecology are always hard to be dealt with and reside in mathematics but not ecology. Aiming at this limitation, the paper further discusses the theorical aspects. Firstly, we begin with the universal optimization in the ecosystem, that is, a complex ecosystem far from equilibrium always tries to find an optimizing process to get the most flux under the certain restriction and cost. Base on this opinion, we discuss the dynamic mechanism of hierarchy forming process in the macroscopic ecosystem from the microcosmic dynamical perspectives. Combing with SOM, we analyze the fractal growth model of subsystems by absorbing flux in the ecosystem whose characters and parameters have been defined by macroscopic measurable parameters. We not only discuss the fractal growth model of ecosystems, but also analyze the fractal dimension and boundary flow of different ecosystems, which inaugurates new ideas and theoretical basis for the evaluation of landscape ecosystem. We consider that the stabilization of pattern in a way is related to a certain attractor in the system. We also use SOM in MATLAB for simulation and reveal a process in which various patterns compete and then become stable under a certain condition. The close one-to-one relation between macroscopic parameters and landscape models has been explored, which provides new facts for the foundations of ecological repair and programming and a guideline for ecological optimization. At last we compare the former investigations with our theory and show the application of sustainable development strategy. We also propose that the industry should reduce flow's resistance through cycle. This paper mainly discusses and simulates the fractal and hierarchy of ecosystem in the ideal view using mathematics and physics and makes a tentative exploring on macroscopic ecosystem. Our theory has some sort of academic and practical values.