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