Ordinary Differential Equations and Dynamical Systems Vol2 · Problem 8.6

Center Manifolds and Bifurcation Theory

Mathematics — Calculus · planar-vector-field-construction

Problem

Let

r = \|x\|

. Construct a

C^1

planar autonomous vector field

f(x)

with an unstable equilibrium at the origin, an asymptotically orbitally stable periodic orbit at

r = 1

, and an orbitally unstable periodic orbit at

r = 2

. Suggestion: Polar coordinates.