Stiffness is defined as the deflection resulting from a force load. An aircraft in straight steady flight has an upwards aerodynamic lift, bending the wing upwards. The longer the wing, the more the wingtip deflects as a result of a certain load. This is the reason why wings with a high aspect ratio bend a lot more.
Removing a bit of wing means that the wing area is reduced and that the aircraft flies with a higher AoA at a certain speed and altitude. It also results in a shorter moment arm for the bending forces, hence less deflection of the wing tip at the same load, hence a higher stiffness.
Wing stiffness is not only defined by the construction of the wing, but also by external influences. This link to @DeltaLima's answer to a similar question provides more background.
Limit cycle oscillation is a form of sustained flutter. From this website:
We discuss the origin of different kinds of limit cycle oscillations. Limit cycle is a trajectory for which energy of the system would be constant over a cycle - i.e. on an average there is no loss or gain of energy.