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Sebastian Wallot, Giuseppe Leonardi
Recurrence plots (RPs) have proved to be a very versatile tool to analyze temporal dynamics of time series data. However, it has also been conjectured that RPs can be used to model samples of random variables, that is, data that do not contain any temporal dependencies. In the current paper, we show that RPs can indeed be used to mimic nonparametric inferential statistics. Particularly, we use the case of the two-sample Kolmogorov-Smirnov test as a proof-of-concept, showing how such a test can be done based on RPs...
August 2018: Chaos
Thales S Lima, Henrique F de Arruda, Filipi N Silva, Cesar H Comin, Diego R Amancio, Luciano da F Costa
Studies regarding knowledge organization and acquisition are of great importance to understand areas related to science and technology. A common way to model the relationship between different concepts is through complex networks. In such representations, networks' nodes store knowledge and edges represent their relationships. Several studies that considered this type of structure and knowledge acquisition dynamics employed one or more agents to discover node concepts by walking on the network. In this study, we investigate a different type of dynamics adopting a single node as the "network brain...
August 2018: Chaos
Denisse Pastén, Zbigniew Czechowski, Benjamín Toledo
We introduce a new method of characterizing the seismic complex systems using a procedure of transformation from complex networks into time series. The undirected complex network is constructed from seismic hypocenters data. Network nodes are marked by their connectivity. The walk on the graph following the time of succeeding seismic events generates the connectivity time series which contains, both the space and time, features of seismic processes. This procedure was applied to four seismic data sets registered in Chile...
August 2018: Chaos
S Oberst, R K Niven, D R Lester, A Ord, B Hobbs, N Hoffmann
Worldwide, mineral exploration is suffering from rising capital costs, due to the depletion of readily recoverable reserves and the need to discover and assess more inaccessible or geologically complex deposits. For gold exploration, this problem is particularly acute. We propose an innovative approach to mineral exploration and orebody characterisation, based on the analysis of geological core data as a spatial dynamical system, using the mathematical tools of dynamical system analysis. This approach is highly relevant for orogenic gold deposits, which-in contrast to systems formed at chemical equilibrium-exhibit many features of nonlinear dynamical systems, including episodic fluctuations on various length and time scales...
August 2018: Chaos
Hwan Bae, Norah Ali, John F Lindner
Certain systems do not completely return to themselves when a subsystem moves through a closed circuit in physical or parameter space. A geometric phase, known classically as Hannay's angle and quantum mechanically as Berry's phase, quantifies such anholonomy. We study the classical example of a bead sliding frictionlessly on a slowly rotating hoop. We elucidate how forces in the inertial frame and pseudo-forces in the rotating frame shift the bead. We then computationally generalize the effect to arbitrary-not necessarily adiabatic-motions...
August 2018: Chaos
Dimitrios Valavanis, Dimitra Spanoudaki, Chrysanthi Gkili, Dimitra Sazou
Recurrence plots (RPs) and recurrence quantification analysis (RQA) are used in this work to study different nonlinear dynamical regimes emerging in an electrochemical system, namely, the electrodissolution-passivation of iron in chloride-containing sulfuric acid solutions. Current oscillations at different applied potentials and chloride concentrations exhibit bifurcations from periodic to complex (bursting) periodic and aperiodic or chaotic behaviors, associated with different dissolution states of iron. The clarification of these transitions is essential to understand the type of corrosion (uniform or localized) taking place as well as the underlying mechanisms governing the stability of the metal...
August 2018: Chaos
Thiago de Lima Prado, Gustavo Zampier Dos Santos Lima, Bruno Lobão-Soares, George C do Nascimento, Gilberto Corso, John Fontenele-Araujo, Jürgen Kurths, Sergio Roberto Lopes
Recurrence analysis and its quantifiers are strongly dependent on the evaluation of the vicinity threshold parameter, i.e., the threshold to regard two points close enough in phase space to be considered as just one. We develop a new way to optimize the evaluation of the vicinity threshold in order to assure a higher level of sensitivity to recurrence quantifiers to allow the detection of even small changes in the dynamics. It is used to promote recurrence analysis as a tool to detect nonstationary behavior of time signals or space profiles...
August 2018: Chaos
Jack Murdoch Moore, Débora Cristina Corrêa, Michael Small
It is rarely possible to precisely characterise the system underlying a series of observations. Hypothesis testing, which involves assessing simple assumptions about driving mechanisms, provides hope that we can at least rule out certain possibilities regarding the nature of the system. Unfortunately, the brevity, nonstationarity, and symbolic nature of certain time series of interest undermines traditional hypothesis tests. Fortunately, recurrence quantification analysis (RQA) has an established record of success in understanding short and nonstationary time series...
August 2018: Chaos
Chenggui Yao, Zhiwei He, Tadashi Nakano, Jianwei Shuai
Neuronal spiking patterns, which are of fundamental importance for the understanding of information processing in neural systems, can be generated in response to different stimuli. We here investigate in detail the stimulus-induced spiking patterns in a biologically plausible neuron model in which the oxygen concentration and the dynamical concentrations of potassium, sodium, and chloride are considered. Various types of spiking patterns can be induced by the different external potassium accumulations in response to the stimulus, including two different types of epileptic seizure (SZ) and spreading depression (SD) states, two different mixed states of SD and SZ, SZ state with multi-burst, and tonic firing behaviors...
August 2018: Chaos
Vladimir Jaćimović, Aladin Crnkić
This paper deals with the low-dimensional dynamics in the general non-Abelian Kuramoto model of mutually interacting generalized oscillators on the 3-sphere. If all oscillators have identical intrinsic generalized frequencies and the coupling is global, the dynamics is fully determined by several global variables. We state that these generalized oscillators evolve by the action of the group <mml:math xmlns:mml=""> <mml:msub> <mml:mi>G</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> of (quaternionic) Möbius transformations that preserve <mml:math xmlns:mml="http://www...
August 2018: Chaos
V C Parro, L Valdo
Actigraphy is a method for monitoring the movements of the nondominant arm, and the technology has found applications ranging from clinical devices to smart wristbands. Time series obtained from actigraphy data is used in chronobiology to define the sleep-wake cycle, as well as in sleep medicine to evaluate an individual's sleep quality. In the study described in this paper, an algorithm based on recurrence quantification analysis (RQA) was applied to a time series obtained from a commercial actigraph, which was used to collect raw data alongside polysomnography (PSG), generally considered as the gold standard for assessing sleep quality...
August 2018: Chaos
K Manikandan, N Vishnu Priya, M Senthilvelan, R Sankaranarayanan
We derive dark and antidark soliton solutions of a parity-time reversal <mml:math xmlns:mml=""> <mml:mo>(</mml:mo> <mml:mrow> <mml:mi>P</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> <mml:mo>)</mml:mo> </mml:math> -invariant variable coefficients nonlocal nonlinear Schrödinger (NNLS) equation. We map the considered equation into a defocusing <mml:math xmlns:mml=""> <mml:mrow> <mml:mi>P</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> -invariant NNLS equation with a constraint between dispersion, nonlinearity, and gain/loss parameters...
August 2018: Chaos
Juan F R Archilla, Yaroslav Zolotaryuk, Yuriy A Kosevich, Yusuke Doi
Some layered silicates are composed of positive ions, surrounded by layers of ions with opposite sign. Mica muscovite is a particularly interesting material, because there exist fossil and experimental evidence for nonlinear excitations transporting localized energy and charge along the cation rows within the potassium layers. This evidence suggests that there are different kinds of excitations with different energies and properties. Some of the authors proposed recently a one-dimensional model based on physical principles and the silicate structure...
August 2018: Chaos
Dadiyorto Wendi, Norbert Marwan
One main challenge in constructing a reliable recurrence plot (RP) and, hence, its quantification [recurrence quantification analysis (RQA)] of a continuous dynamical system is the induced noise that is commonly found in observation time series. This induced noise is known to cause disrupted and deviated diagonal lines despite the known deterministic features and, hence, biases the diagonal line based RQA measures and can lead to misleading conclusions. Although discontinuous lines can be further connected by increasing the recurrence threshold, such an approach triggers thick lines in the plot...
August 2018: Chaos
Wilten Nicola, Peter John Hellyer, Sue Ann Campbell, Claudia Clopath
Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general mechanism for the emergence of low dimensional dynamics remains elusive. Here, we consider Wilson-Cowan networks and demonstrate through numerical and analytical work that homeostatic regulation of the network firing rates can paradoxically lead to a rich dynamical repertoire. The dynamics include mixed-mode oscillations, mixed-mode chaos, and chaotic synchronization when the homeostatic plasticity operates on a moderately slower time scale than the firing rates...
August 2018: Chaos
Hanqing Wang, Jun Wang, Guochao Wang
The exploration of return volatility dynamics is of great significance to evaluate investment risk, avoid stock market crisis, and purchase stock portfolio. In this paper, we propose a novel concept to characterize the fluctuation duration of stock markets, which is continuous fluctuation intensity (CFI). The CFI represents the duration for continuous increasing or decreasing return volatilities (or normalized absolute returns) above or below a previous day's value. Distinguished from previous studies, the CFI does not need to set a threshold in advance but to select the sequence of return volatilities that are continuously growing or falling in the series...
August 2018: Chaos
Yongwang Gong, Michael Small
Epidemic dynamics in a structured population has been widely investigated in recent years by utilizing the metapopulation framework with a reaction-diffusion approach. In this paper, we study epidemic spreading on metapopulation networks, including migration and demographics, wherein population dynamics in each node (a patch) follows the logistic model with a heterogeneous carrying capacity. The epidemic threshold is theoretically calculated at a mean-field level and is then evaluated by Monte Carlo simulations...
August 2018: Chaos
A S Karavaev, A R Kiselev, A E Runnova, M O Zhuravlev, E I Borovkova, M D Prokhorov, V I Ponomarenko, S V Pchelintseva, T Yu Efremova, A A Koronovskii, A E Hramov
We study the synchronization of infra-slow oscillations in human scalp electroencephalogram signal with the respiratory signal. For the cases of paced respiration with a fixed frequency and linearly increasing frequency, we reveal the phase and frequency locking of infra-slow oscillations of brain potentials by respiration. It is shown that for different brain areas, the infra-slow oscillations and respiration can exhibit synchronous regimes of different orders.
August 2018: Chaos
David Hartman, Jaroslav Hlinka
Stock networks, constructed from stock price time series, are a well-established tool for the characterization of complex behavior in stock markets. Following Mantegna's seminal paper, the linear Pearson's correlation coefficient between pairs of stocks has been the usual way to determine network edges. Recently, possible effects of nonlinearity on the graph-theoretical properties of such networks have been demonstrated when using nonlinear measures such as mutual information instead of linear correlation. In this paper, we quantitatively characterize the nonlinearity in stock time series and the effect it has on stock network properties...
August 2018: Chaos
Soumen Majhi, Dibakar Ghosh
The distinctive phenomenon of the chimera state has been explored in neuronal systems under a variety of different network topologies during the last decade. Nevertheless, in all the works, the neurons are presumed to interact with each other directly with the help of synapses only. But, the influence of ephaptic coupling, particularly magnetic flux across the membrane, is mostly unexplored and should essentially be dealt with during the emergence of collective electrical activities and propagation of signals among the neurons in a network...
August 2018: Chaos
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