Weakly dissipative system

1
Weakly dissipative system local analysis
Linear stability analysis
or
Hopf bifurcation
saddlenode
S /U upper state exists and is
stable/unstable S/U lower state exists and
is stable/unstable
intermediate state (unstable) exists at
Hopf ()
Hopf ()
2
Weakly dissipative system global analysis
Trajectories at d? 0,
Conserved energy
energy change
At small d compute the rate of energy change by
averaging over the period T
integration limits are values of y at turning
points where p vanishes
3
Weakly dissipative system global analysis
Condition for a stationary orbit
Value of m required for a stationarity
Bifurcation diagram
sniper
1
2

1. ()
2. O
3. O ()
4. ()
5. () o
6. ()()
7. () o
8. ()

3
4
5
6
7
8