Phase locking in on-off intermittency

Complete periodic synchronization in coupled systems

Recently, complete chaotic synchronization in coupled systems has been well studied. In this paper, we study complete synchronization in coupled periodic oscillators with diffusive and gradient couplings. Eight typical types of critical curve for the transverse Lyapunov exponent of standard mode, which give rise to different synchronization-desynchronization patterns, are classified. All possible desynchronous behaviors including steady state, periodic state, quasiperiodic state, low-dimensional chaotic state, and two types of high-dimensional chaotic state are identified, and two classical synchronization-desynchronizaiton bifurcations--the shortest wavelength bifurcation and Hopf bifurcation from synchronous periodic state--are classified.

On-off intermittency in earthquake occurrence

The clustered occurrence of earthquakes is viewed as an intermittent phenomenon, interpreting the clusters of events as chaotic bursts combined to the Poissonian occurrence of background seismicity. In particular, we suggest that it can be interpreted as an example of on-off intermittency. This kind of intermittency is parameter driven and exhibits certain universal statistical properties. The study of a Californian catalogue allows to interpret earthquake occurrence as an on-off intermittent phenomenon. Our results suggest the existence of a branching mechanism in earthquake occurrence well explained by epidemic type models.

Synchronization of chaotic systems with coexisting attractors

Synchronization of coupled oscillators exhibiting the coexistence of chaotic attractors is investigated, both numerically and experimentally. The route from the asynchronous motion to a completely synchronized state is characterized by the sequence of type-I and on-off intermittencies, intermittent phase synchronization, anticipated synchronization, and period-doubling phase synchronization.

Frequency-locking phenomena of propagating wave fronts in reaction-diffusion systems

We observe N:(N-1)(N>/=2) frequency-locking phenomena of propagating wave fronts when increasing the light intensity in a spatially extended system. The experiments were carried out using the light-sensitive form of the Belousov-Zhabotinsky reaction with Ru(bpy)(2+)3 as a catalyst. By constructing a mapping function, the characteristic devil's staircase can be reproduced when plotting wave period versus light intensity, in agreement with the experimental data.

Logarithmic periodicities in the bifurcations of type-I intermittent chaos

The critical relations for statistical properties on saddle-node bifurcations are shown to display undulating fine structure, in addition to their known smooth dependence on the control parameter. A piecewise linear map with the type-I intermittency is studied and a log-periodic dependence is numerically obtained for the average time between laminar events, the Lyapunov exponent, and attractor moments. The origin of the oscillations is built in the natural probabilistic measure of the map and can be traced back to the existence of logarithmically distributed discrete values of the control parameter giving Markov partition. Reinjection and noise effect dependences are discussed and indications are given on how the oscillations are potentially applicable to complement predictions made with the usual critical exponents, taken from data in critical phenomena.

Coherence resonance near the Hopf bifurcation in coupled chaotic oscillators

We uncover a coherence resonance near the Hopf bifurcation from chaos in coupled chaotic oscillators. At the bifurcation, a nearly periodic rotating wave becomes stable as the state of synchronous chaos is destabilized. We find that noise can induce the bifurcation and, more strikingly, it can enhance the temporal regularity of the wave pattern in the coupled system. This resonant phenomenon is expected to be robust and physically observable.