A limit cycle encloses nodes, F spirals, C centres, and S saddle points only, all of the linear type of Section 2.5. Show that N + F + C – S = 1  1. Given the system whereαis a parameter, prove that...

A limit cycle encloses nodes, F spirals, C centres, and S saddle points only, all of the linear type of Section 2.5. Show that N + F + C – S = 1

1. Given the system

whereαis a parameter, prove that the index of a simple closed curve which does not meet an equilibriumpoint is independent ofα(See also Problem 2.41).