Qualitative analysis of nn-dimensional competitive systems

In this paper, a n-dimensional cubic competitive model with characteristic of “better for better” is presented to investigate the phenomenon of “winner-take-all”. The singular points and singular curve of the system are obtained by calculating the intersection points of isoclinic curved surfaces, their types are also gotten. Then the definition regions of the system are divided into several invariant regions by invariant hyperplanes. The global quality of the system are discussed by analyzing the tendencies of trajectories in every invariant regions. Lastly the result is applied to analyze the competition among n e-commerce web sites and constraint conditions of coexistence or annihilation are obtained.