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## Homework Statement

Find whether this system is stable or unstable at the steady state (x1,x2)=(0,0)

dx

_{1}/dt = -x

_{1}+2sin(x

_{1})+x

_{2}

dx

_{2}/dt=2sin(x

_{2})

## Homework Equations

## The Attempt at a Solution

z

_{1}=x

_{1}-0

z

_{2}=x

_{2}-0

dz

_{1}/dt=-z

_{1}+z

_{2}+2z

_{1}

dz

_{2}/dt=2z

_{2}

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 z

_{1}is set equal to x

_{1}(I believe this is called linearization)? Could someone please clarify this step for me and how on earth

dx

_{2}/dt=2sin(x

_{2}) becomes dz

_{2}/dt=2z

_{2}?

The rest is pretty straightforward.