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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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.
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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