Rn. Iyengar et D. Roy, EXTENSIONS OF THE PHASE-SPACE LINEARIZATION (PSL) TECHNIQUE FOR NONLINEAR OSCILLATORS, Journal of sound and vibration, 211(5), 1998, pp. 877-906
This paper is devoted to further exploration of the PSL technique deve
loped earlier in its companion paper. To start with, it is shown that
the method is not only appicable for obtaining one-periodic orbits, bu
t can be made use of for obtaining every conceivable orbit, including
subharmonic or period-doubled orbits, quasi-periodic orbits and even c
haotic orbits. This is numerically illustrated by constructing various
such orbits of Ueda's, Duffing-Holmes' and Van der Pol's oscillators.
Next, the separatrix, that separates the basins of attraction of the
stable limit cycles of Duffing-Holmes' oscillator, is constructed usin
g the PSL procedure. A possibility of predicting the chaotic diffusion
of trajectories based on a heuristic argument of a near-tangency of s
table and unstable limit cycles of Duffing-Holmes' oscillator is also
discussed. Finally, the PSL scheme is made use of to compute various c
haracteristic quantities such as Fourier spectra, Liapunov characteris
tic exponents and probability density functions. Many new results are
presented to establish the versatility of the PSL method. (C) 1998 Aca
demic Press Limited.