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The global behavior of the system is characterized by bifurcation diagrams that identify the instabilities that appear when one of the excitations is slowly varied.
In an MR spectrometer (Figure 2) the amount of energy extracted from the superimposed field is continuously measured and recorded on a strip chart while the frequency of the field is slowly varied.
We find that a properly designed, slowly varied input leading edge can reduce the output up-shoot drastically in a single-channel condition, while in a multi-channel condition, a gradually changed input waveform can eliminate the abrupt power up-shoot due to forward signal-to-signal Raman interactions and obtain a better gain clamping result by using pump adjustment.
As parameters are slowly varied, steady state instabilities may occur; these can include jumps to resonance, subharmonic period-doubling bifurcations, cascades to chaos, etc. Moreover a sudden pulse of excitation may lead to a transient failure of the system.
Typically during experiments, however, the magnetic field is slowly varied or held constant for a few minutes, and swept between zero and some high field strength, and then the cooling plant does not pose limits to the operation.
This paper presents the extended Lindstedt Poincare (EL P) method, which applies multiple time variables to treat non-stationary oscillations arising in dynamical systems with cubic nonlinearities due to the slowly varied excitation parameters.
Similar(54)
All the coefficients b k for k≠0 slowly vary with k, b k+1≃b k, the slow varying nature of b k is the key motivation for self ICI cancelation [19].
Again, the smoothly varying (marked with a tilde) terms in Equation (3) enter because the constant of proportionality may slowly vary with n, for example because the initial neutral cluster size distribution has a finite width, detection efficiencies may depend on n, and so forth.
We consider a periodic Schrödinger operator in two dimensions perturbed by a weak magnetic field whose intensity slowly varies around a positive mean.
It is an iterative procedure that helps to slowly vary a "temperature" or "nonlinearity parameter" λ while iterating to improve on an estimate of the Riemann spectrum of the input data.
It is assumed that κ is either constant or slowly varies with ∆T.
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