Stochastic analysis of recurrence plots with applications to the detection of deterministic signals

Rohde, Gustavo K.; Nichols, Jonathan M.; Dissinger, Bryan M.; Bucholtz, F.

doi:10.1016/j.physd.2007.10.008

Cited by 29 publications

(16 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In addition to that, there are some different and useful ways to define the RQA analysis, as was done in [5], relating the statistics obtained from an unthreshold recurrence plot (a specific kind of recurrence quantification that does not impose the threshold ε, but deals with the distance among the points in the recurrence matrix) to first-and second-order statistics of the time series. This approach claims to be a more robust (in terms of recurrence plot parameters) and efficient deterministic signal detector than classical RQA measures, although it would require several mixtures in order to establish an adequate statistics.…”

Section: Discussionmentioning

confidence: 99%

“…13 shows one of the observed mixtures, while the middle and lower pan- Table 2 Mean ± standard deviation (σ ) of the obtained MSE given by the solutions in the underdetermined scenario provided for the different score functions in 100 trails. MSE d , MSE l , MSE e , MSE k and MSE w refer, respectively, to the mean-squared error for the solutions obtained with the (2), (3), (4), (5) and Wiener paradigm. WG, WU, CG refer, respectively, to white gaussian, uniform and exponential correlated gaussian stochastic sources.…”

Section: Blind Extraction In An Underdetermined Scenariomentioning

confidence: 99%

“…In fact, distinguishing chaotic from random signals is a far from trivial task, especially when experimental time series immersed in noise are considered [2][3][4][5]. The most common approach is to evaluate the Kolmogorov-Sinai (KS) entropy by calculating its lower bound given by the correlation entropy (K2) [6].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Blind extraction of chaotic sources from mixtures with stochastic signals based on recurrence quantification analysis

Soriano

Suyama

Attux

2011

Digital Signal Processing

View full text Add to dashboard Cite

Section: Discussionmentioning

confidence: 99%

Section: Blind Extraction In An Underdetermined Scenariomentioning

confidence: 99%

See 1 more Smart Citation

Blind extraction of chaotic sources from mixtures with stochastic signals based on recurrence quantification analysis

Soriano

Suyama

Attux

2011

Digital Signal Processing

View full text Add to dashboard Cite

“…However, the choice of a different norm would not change the presented results qualitatively. The properties of RPs have been intensively studied for different kinds of dynamics [13], including periodic, quasiperiodic [17][18][19], chaotic, and stochastic dynamics [20,21]. It has been shown that, among other features, the length distributions of diagonal and vertical structures in RPs can be used for defining a variety of measures of complexity, which characterize properties such as the degree of determinism or laminarity of the system [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

Zou

Donner

Kurths

2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Rössler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral-and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given. PACS numbers:Oscillatory processes can be frequently observed in natural and technological systems. Often, the corresponding dynamics is not strictly periodic, but shows more complex temporal variability patterns characterized by a fast divergence of trajectories with arbitrarily close initial conditions [1-3]. There are numerous examples of such chaotic oscillators for which long-term predictions of amplitudes and phases are not possible. Therefore, studying their phase dynamics has recently attracted particular interest, e.g., regarding the process of phase synchronization between different coupled systems [4,5]. However, most existing methods suitable for this purpose require the explicit definition of an appropriate phase variable, which can become a non-trivial problem in the case of noncoherent chaotic oscillations. Therefore, studying the phase coherence properties of chaotic systems has become an important problem in both theoretical and experimental studies [6]. In this work, we propose some methods based on the concept of recurrences in phase space, which allow studying complementary aspects of chaotic oscillators relating to the geometric structure of, and the dynamics on the attractor. Specifically, we derive a detailed characterization of changes of the geometric structure of complex systems in phase space with varying control parameter, which accompany transitions from phase-coherent to noncoherent dynamics.

show abstract

“…However, very few applications of recurrence plots were reported in signal processing -mostly in speech processing and signal detection (e.g. [4,5,6,7]). The integration of this technique in the signal processing field seems natural, as there is a strong similarity between recurrence and frequency.…”

Section: Introductionmentioning

confidence: 99%

On the recurrence plot analysis method behaviour under scaling transform

Birleanu

Ioana

Gervaise

et al. 2011

2011 IEEE Statistical Signal Processing Workshop (SSP)

View full text Add to dashboard Cite

In the last decade, the applications of the recurrence plot analysis method make it a valuable alternative to the time-frequency and time-scale tools. As it was initially developed for the study of dynamical systems, and was later used in nonlinear time series analysis, the question of using it as a signal processing tool has not been put into discussion yet. In this field the projective techniques are largely used, with good results. Nevertheless, they also have some limitations -especially regarding transient signal processing. But this kind of signals are ubiquitous in real world. In addition, propagation through various media as well as on multiple paths lead to delayed, attenuated and dilated versions of the original transients. In this paper we study the behaviour of the recurrence plot analysis method in the context of analyzing some finite duration signals being subject to rescalings of the amplitude and time axes. This study is a starting point in employing the analysis of recurrences in investigations of a large class of real world signals.

show abstract

Stochastic analysis of recurrence plots with applications to the detection of deterministic signals

Cited by 29 publications

References 18 publications

Blind extraction of chaotic sources from mixtures with stochastic signals based on recurrence quantification analysis

Blind extraction of chaotic sources from mixtures with stochastic signals based on recurrence quantification analysis

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

On the recurrence plot analysis method behaviour under scaling transform

Contact Info

Product

Resources

About