32 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
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