Flows with collective dynamics on a sphere

Abstract

In this article different properties of flow codes are studied and a diagram is constructed as a whole topological invariant of them. In particular, flows with no more than 6 saddles are described. Two types of simple bifurcations: positive and negative – are considered as well. Summarizing the results on compact surfaces with boundary remains an interesting question for future works.

Keywords

• flows
• collective dynamics
• topological invariant
• simple bifurcations