EXTENSIONS OF THE PHASE-SPACE LINEARIZATION (PSL) TECHNIQUE FOR NONLINEAR OSCILLATORS

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.