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Homework Statement
Find whether this system is stable or unstable at the steady state (x1,x2)=(0,0)
dx1/dt = -x1+2sin(x1)+x2
dx2/dt=2sin(x2)
Homework Equations
The Attempt at a Solution
z1=x1-0
z2=x2-0
dz1/dt=-z1+z2+2z1
dz2/dt=2z2
Jacobian =
[ 1 1 ]
[ 0 2 ]
so the system is unstable.
This problem is from my notes from class; I'm not 100% certain that it is written correctly. I am very confused about the part where z1 is set equal to x1 (I believe this is called linearization)? Could someone please clarify this step for me and how on earth
dx2/dt=2sin(x2) becomes dz2/dt=2z2 ?
The rest is pretty straightforward.