Consider the system i1 = x – 2x1x2 and i2 = -x2 + xí a. Find the first few terms in the power series expansion of the stable center manifolds at the origin. b. Find the reduced dynamics on the center manifold. Discuss the stab of the equilibrium. Numerically compute solutions in the phase plane and relate it to
Consider the system i1 = x – 2x1x2 and i2 = -x2 + xí a. Find the first few terms in the power series expansion of the stable center manifolds at the origin. b. Find the reduced dynamics on the center manifold. Discuss the stab of the equilibrium. Numerically compute solutions in the phase plane and relate it to
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![2. Consider the system i1 = x – 2x1x2 and i2 = -x2 + xỉ
|
a. Find the first few terms in the power series expansion of the stable and
center manifolds at the origin.
b. Find the reduced dynamics on the center manifold. Discuss the stability
of the equilibrium.
c. Numerically compute solutions in the phase plane and relate it to your
solution to the previous two problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F592c0487-d9db-444f-8a0b-2c812607553a%2Fabd30915-2b42-4e93-8c6b-6e0f170b9f52%2F4oc3r7d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Consider the system i1 = x – 2x1x2 and i2 = -x2 + xỉ
|
a. Find the first few terms in the power series expansion of the stable and
center manifolds at the origin.
b. Find the reduced dynamics on the center manifold. Discuss the stability
of the equilibrium.
c. Numerically compute solutions in the phase plane and relate it to your
solution to the previous two problems.
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