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Different routes to chaos via strange nonchaotic attractor in a quasiperiodically forced system
This paper focusses attention on the strange nonchaotic attractors (SNA) of a
quasiperiodically forced dynamical system. Several routes, including the
standard ones by which the appearance of strange nonchaotic attractors takes
place, are shown to be realizable in the same model over a two parameters
() domain of the system. In particular, the transition through
torus doubling to chaos via SNA, torus breaking to chaos via SNA and period
doubling bifurcations of fractal torus are demonstrated with the aid of the two
parameter () phase diagram. More interestingly, in order to
approach the strange nonchaotic attractor, the existence of several new
bifurcations on the torus corresponding to the novel phenomenon of torus
bubbling are described. Particularly, we point out the new routes to chaos,
namely, (1) two frequency quasiperiodicity torus doubling torus
merging followed by the gradual fractalization of torus to chaos, (2) two
frequency quasiperiodicity torus doubling wrinkling SNA
chaos SNA wrinkling inverse torus doubling torus
torus bubbles followed by the onset of torus breaking to chaos via SNA or
followed by the onset of torus doubling route to chaos via SNA. The existence
of the strange nonchaotic attractor is confirmed by calculating several
characterizing quantities such as Lyapunov exponents, winding numbers, power
spectral measures and dimensions. The mechanism behind the various bifurcations
are also briefly discussed.Comment: 12 pages, 12 figures, ReVTeX (to appear in Phys. Rev. E
Bifurcation and chaos in the double well Duffing-van der Pol oscillator: Numerical and analytical studies
The behaviour of a driven double well Duffing-van der Pol (DVP) oscillator
for a specific parametric choice () is studied. The
existence of different attractors in the system parameters () domain
is examined and a detailed account of various steady states for fixed damping
is presented. Transition from quasiperiodic to periodic motion through chaotic
oscillations is reported. The intervening chaotic regime is further shown to
possess islands of phase-locked states and periodic windows (including period
doubling regions), boundary crisis, all the three classes of intermittencies,
and transient chaos. We also observe the existence of local-global bifurcation
of intermittent catastrophe type and global bifurcation of blue-sky catastrophe
type during transition from quasiperiodic to periodic solutions. Using a
perturbative periodic solution, an investigation of the various forms of
instablities allows one to predict Neimark instablity in the plane
and eventually results in the approximate predictive criteria for the chaotic
region.Comment: 15 pages (13 figures), RevTeX, please e-mail Lakshmanan for figures,
to appear in Phys. Rev. E. (E-mail: [email protected]
The radial gradient of interplanetary radiation measured by Mariners 4 and 5
Interplanetary radiation radial gradient measured from Mariners 4 and
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