Ordinary Differential Equations and Dynamical Systems Vol2 · Problem 8.3

Center Manifolds and Bifurcation Theory

Mathematics — Calculus · averaging-critical-perturbation

Problem

Consider the system x1′=x2+ε(x12sin⁡t−sin⁡t),x2′=−x1.x_1' = x_2 + \varepsilon(x_1^2 \sin t - \sin t), \quad x_2' = -x_1. (a) Verify that this is a critical perturbation. (b) Compute a Lagrange standard form for this system. (c) Find the corresponding averaged equations. (d) What does the averaged system say about the existence and stability of periodic solutions?

Browse the problem library