Directed recurrence networks for the analysis of nonlinear and complex dynamical systems.

Complex network approaches have been emerging as an analysis tool for dynamical systems. Different reconstruction methods from time series have been shown to reveal complicated behaviors that can be quantified from the network's topology. Directed recurrence networks have recently been suggested as one such method, complementing the already successful recurrence networks and expanding the applications of recurrence analysis.

A bottom-up approach for recurrence detection based on sampling distance.

One of the major problems faced in the recurrence analysis of dynamical systems is the tangential motion effect affecting the structures in recurrence plots and their quantification. This issue roots to the choice of a threshold for recurrence, making it a crucial parameter for such analyses. It has been shown that a variable threshold following the dynamical changes of the system is more suited to the analysis of non-stationary data as it mitigates this effect.

Directed recurrence networks.

Complex network approaches have attracted a growing interest in the analysis of nonlinear time series. Among other reconstruction methods, it has been shown that the recurrence plot can be used as the adjacency matrix for recurrence networks, expanding the applications of the already successful recurrence analysis. We study here the potential benefits of a directed formulation of recurrence networks through a simple modification of the recurrence plot.

A variable threshold for recurrence based on local attractor density.

Recurrence plots along with their quantification measures have demonstrated their usefulness for the study of dynamical systems in many fields. The distance threshold for recurrence is a crucial parameter influencing the observed recurrence structures, thus, the related quantification measures, and have been the object of several studies to find its optimal value. We suggest here a definition of recurrence based on the local attractor density to obtain more qualitative recurrence plots capturing the dynamics at different scales without suffering from variations in the tangential motion effect.

Observation of thermoacoustic chaotic oscillations in a looped tube.

This study presents experimental observations of chaotic thermoacoustic oscillations induced in a looped tube with respect to both temporal and spatial dimensions and compares them with those in a resonance tube system. The wave propagation directions observed in thermoacoustic systems showing periodic behaviors are confirmed in the chaotic case, from cold to hot sides in the stack in a looped system, and with reflections at the ends of a resonance tube system. Although both systems are similar in their route to chaos and correlation dimensions of the chaotic attractor, a recurrence visualization method reveals differences in the distribution of temporal patterns resulting from the mode competition between the natural frequencies of the systems.

Bifurcation diagram of coupled thermoacoustic chaotic oscillators.

A thermoacoustic chaotic oscillator is a fluid system that presents thermally induced chaotic oscillations of a gas column. This study experimentally reports a bifurcation diagram when two thermoacoustic chaotic oscillators are dissipatively coupled to each other. The two-parameter bifurcation diagram is constructed by varying the frequency mismatch and the coupling strength.

On-off intermittency in coupled chaotic thermoacoustic oscillations.

This paper documents on-off intermittency observed in coupled thermoacoustic chaotic oscillations. Mode competition between two or three oscillation modes engenders chaotic oscillations through quasiperiodic oscillations introduced by a local cross-sectional change in a gas-filled tube. Complete synchronization is then obtained by connecting two thermoacoustic chaotic oscillators via a rigid plate with an orifice.