4,420 research outputs found
Peeling Bifurcations of Toroidal Chaotic Attractors
Chaotic attractors with toroidal topology (van der Pol attractor) have
counterparts with symmetry that exhibit unfamiliar phenomena. We investigate
double covers of toroidal attractors, discuss changes in their morphology under
correlated peeling bifurcations, describe their topological structures and the
changes undergone as a symmetry axis crosses the original attractor, and
indicate how the symbol name of a trajectory in the original lifts to one in
the cover. Covering orbits are described using a powerful synthesis of kneading
theory with refinements of the circle map. These methods are applied to a
simple version of the van der Pol oscillator.Comment: 7 pages, 14 figures, accepted to Physical Review
Deterministic polarization chaos from a laser diode
Fifty years after the invention of the laser diode and fourty years after the
report of the butterfly effect - i.e. the unpredictability of deterministic
chaos, it is said that a laser diode behaves like a damped nonlinear
oscillator. Hence no chaos can be generated unless with additional forcing or
parameter modulation. Here we report the first counter-example of a
free-running laser diode generating chaos. The underlying physics is a
nonlinear coupling between two elliptically polarized modes in a
vertical-cavity surface-emitting laser. We identify chaos in experimental
time-series and show theoretically the bifurcations leading to single- and
double-scroll attractors with characteristics similar to Lorenz chaos. The
reported polarization chaos resembles at first sight a noise-driven mode
hopping but shows opposite statistical properties. Our findings open up new
research areas that combine the high speed performances of microcavity lasers
with controllable and integrated sources of optical chaos.Comment: 13 pages, 5 figure
Variations of Boundary Surface in Chua’s Circuit
The paper compares the boundary surfaces with help of cross-sections in three projection planes, for the four changes of Chua’s circuit parameters. It is known that due to changing the parameters, the Chua’s circuit can be characterized in addition to a stable limit cycle also by one double scroll chaotic attractor, two single scroll chaotic attractors or other two stable limit cycles. Chua’s circuit can even start working as a binary memory. It is not known yet, how changes in parameters and conseqently in attractors in the circuit will affect the morphology of the boundary surface. The boundary surface separates the double scroll chaotic attractor from the stable limit cycle. In a variation of the parameters presented in this paper the boundary surface will separate even single scroll chaotic attractors from each other. Dividing the state space into regions of attractivity for different attractors, however, remains fundamentally the same
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