Evolutionary dynamics of systems

Nonlinear systems with positive feedback will make the system to evolve under natural selection and human intervention with limited resources. The behaviors of evolution might be very complicated. In order to describe complexity, fractal modelings are usually appropriate. The evolution of a system from generation to generation is moving toward an attractor which might be a point or a set of patterns. During the evolution, quantitative changes as well as qualitative changes are both possible. Phase transition which is the boundary of two attracting basins is a turning point for qualitative change. In order to control the evolution toward a better condition, searching for a better solution among alternatives, of which the number of possibilities is huge, is the purpose of human intervention. Therefore, positive feedback, fractal, attractors and phase transition, and searching for better are the main issues of the evolutionary dynamics of systems.