724 research outputs found
Design strategies for the creation of aperiodic nonchaotic attractors
Parametric modulation in nonlinear dynamical systems can give rise to
attractors on which the dynamics is aperiodic and nonchaotic, namely with
largest Lyapunov exponent being nonpositive. We describe a procedure for
creating such attractors by using random modulation or pseudo-random binary
sequences with arbitrarily long recurrence times. As a consequence the
attractors are geometrically fractal and the motion is aperiodic on
experimentally accessible timescales. A practical realization of such
attractors is demonstrated in an experiment using electronic circuits.Comment: 9 pages. CHAOS, In Press, (2009
Enhancing synchronization in chaotic oscillators by induced heterogeneity
We report enhancing of complete synchronization in identical chaotic
oscillators when their interaction is mediated by a mismatched oscillator. The
identical oscillators now interact indirectly through the intermediate relay
oscillator. The induced heterogeneity in the intermediate oscillator plays a
constructive role in reducing the critical coupling for a transition to
complete synchronization. A common lag synchronization emerges between the
mismatched relay oscillator and its neighboring identical oscillators that
leads to this enhancing effect. We present examples of one-dimensional open
array, a ring, a star network and a two-dimensional lattice of dynamical
systems to demonstrate how this enhancing effect occurs. The paradigmatic
R\"ossler oscillator is used as a dynamical unit, in our numerical experiment,
for different networks to reveal the enhancing phenomenon.Comment: 10 pages, 7 figure
Enhancing Synchrony in Chaotic Oscillators by Dynamic Relaying
In a chain of mutually coupled oscillators, the coupling threshold for
synchronization between the outermost identical oscillators decreases when a
type of impurity (in terms of parameter mismatch) is introduced in the inner
oscillator(s). The outer oscillators interact indirectly via dynamic relaying,
mediated by the inner oscillator(s). We confirm this enhancing of critical
coupling in the chaotic regimes of R\"ossler system in absence of coupling
delay and in Mackey-Glass system with delay coupling. The enhancing effect is
experimentally verified in electronic circuit of R\"ossler oscillators.Comment: 4 pages, 9 figure
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