Type-I intermittency with noise versus eyelet intermittency

Horizontal visibility graphs generated by type-I intermittency.

The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associated HV graphs. We show how the alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure...

On-off intermittency in small neural networks with synaptic noise

Attractor-Repeller Collision and Eyelet Intermittency at the Transition to Phase Synchronization

The chaotically driven circle map is considered as the simplest model of phase synchronization of a chaotic continuous-time oscillator by external periodic force. The phase dynamics is analyzed via phase-locking regions of the periodic cycles embedded in the strange attractor. It is shown that full synchronization, where all the periodic cycles are phase locked, disappears via the attractor-rep...

Influence of noise on scalings for in-out intermittency.

We study the effects of noise on a recently discovered form of intermittency, referred to as in-out intermittency. This type of intermittency, which reduces to on-off in systems with a skew product structure, has been found in the dynamics of maps, (ODE) and (PDE) simulations that have symmetries. It shows itself in the form of trajectories that spend a long time near a symmetric state interspe...

Low-frequency noise controls on-off intermittency of bifurcating systems.

A bifurcating system subject to multiplicative noise can display on-off intermittency. Using a canonical example, we investigate the extreme sensitivity of the intermittent behavior to the nature of the noise. Through a perturbative expansion and numerical studies of the probability density function of the unstable mode, we show that intermittency is controlled by the ratio between the departur...