Perturbation Analysis of a Kind of Information Processing Systems

摘要

For a plane vector field with singular point which smooth dependent on parameters , when the parameter changes, the change of the number of the singular point and the change of the structure of orbit near the singular point is singular point bifurcation phenomena that we care about. If the singular point of the vector field is degenerate, the number of the singular point is unchanged, at the same time parameter changes tiny in the same position, under the singular points smooth rely on the change of the parameter. If singular point of the vector field is degradation, by any small disturbance singular points change into the degenerate points or disappear. The singular point bifurcation problem of the vector field can be converted into discussing zero number of bifurcation function and the singular point topological structure problems of the corresponding system in the orbit near the singular point. And then simplify the perturbation analysis, get the structure stability of the system .