A coefficient proportional to 1 minus x-squared represents this phenomenon in the equation of motion of a Van der Pol oscillator, which can be shown to have a unique limit cycle via Liénard’s theorem. For 10 points each:
[10m] Name this phenomenon that corresponds to the first-order term for a linear oscillator. The Q factor measures how far a system is below its “critical” level of this phenomenon.
ANSWER: damping [accept word forms like damped; reject “dampening”]
[10e] Unlike the Van der Pol oscillator, most nonlinear damped and driven systems exhibit multiple attractors, a characteristic of systems with this property. The double pendulum is a classic example of a system that exhibits this property of extreme sensitivity to initial conditions.
ANSWER: chaos [or chaotic]
[10h] Oscillators with infinitely many attractors often exhibit chaos via a “cascade” of these phenomena. The limiting ratios between these phenomena, which may be viewed on a bifurcation diagram, is given by the first Feigenbaum constant.
ANSWER: period-doublings [accept period-doubling cascades or period-doubling bifurcations]
<JC, Physics>