68 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
Coexisting synchronous and asynchronous states in locally coupled array of oscillators by partial self-feedback control
We report the emergence of coexisting synchronous and asynchronous
subpopulations of oscillators in one dimensional arrays of identical
oscillators by applying a self-feedback control. When a self-feedback is
applied to a subpopulation of the array, similar to chimera states, it splits
into two/more sub-subpopulations coexisting in coherent and incoherent states
for a range of self-feedback strength. By tuning the coupling between the
nearest neighbors and the amount of self-feedback in the perturbed
subpopulation, the size of the coherent and the incoherent sub-subpopulations
in the array can be controlled, although the exact size of them is
unpredictable. We present numerical evidence using the Landau-Stuart (LS)
system and the Kuramoto-Sakaguchi (KS) phase model.Comment: 13 pages, 13 figures, accepted for publication in CHAOS (July 2017
Lag synchronization and scaling of chaotic attractor in coupled system
We report a design of delay coupling for lag synchronization in two
unidirectionally coupled chaotic oscillators. A delay term is introduced in the
definition of the coupling to target any desired lag between the driver and the
response. The stability of the lag synchronization is ensured by using the
Hurwitz matrix stability. We are able to scale up or down the size of a driver
attractor at a response system in presence of a lag. This allows compensating
the attenuation of the amplitude of a signal during transmission through a
delay line. The delay coupling is illustrated with numerical examples of 3D
systems, the Hindmarsh-Rose neuron model, the R\"ossler system and a Sprott
system and, a 4D system. We implemented the coupling in electronic circuit to
realize any desired lag synchronization in chaotic oscillators and scaling of
attractors.Comment: 10 pages, 7 figure
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