Fluctuations close to periodic motion
of self-oscillating systems.
b) Melnikov method is used in case of periodic motions
and is analysing the conditions necessary in order for the stable and non-stable varieties of the same hyperbolic point to transversally intersect each odder.
The periodic motion
of the sphere behind the advancing free surface is obvious from this plot.
Heller, now at Harvard University, argued on theoretical grounds that quantum particles in such a geometry would have eigenfunctions that retain some of the wave patterns associated with regular, periodic motion
Taking advantage of a chaotic system's extreme sensitivity to initial conditions, they use a series of tiny, judiciously chosen and carefully applied perturbations to maneuver its behavior into the type of periodic motion
It clearly exhibits the hallmark of a chaotic system -- that is, getting continuously thrown from one periodic motion
to another," Rauseo says.
According to their simple model, gusts of wind initially act as a random buffeting force on a suspension bridge, causing the towers and main cable to go into a high-frequency periodic motion
like that of a randomly struck guitar string.
At other times, I can get it doing simple periodic motion
[like a pendulum] or more complicated periodic motions
1965, On the existence of almost periodic motions
, Michigan Math.