Detecting determinism using recurrence quantification analysis: Three test procedures

Aparicio, Teresa; Pozo, Eduardo F.; Saura, Dulce

doi:10.1016/j.jebo.2006.03.005

Cited by 34 publications

(34 citation statements)

References 21 publications

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“…S2). Additional tests for determinism have been defined by Aparicio (37). Applying these, we found significant evidence for determinism in all Nod factor-treated and mycorrhizal-treated cells analyzed (Table 1).…”

Section: Rhizobial Bacteria and Mycorrhizal Fungi Induce Differentialmentioning

confidence: 67%

“…Three tests for determinism (37) were run on 1 dimensional recurrence plots of the time series. A recurrence was identified at 0.5 times the standard deviation, or in cases where this produced more recurrences than nonrecurrence, the tolerance was set to 0.1 times the standard deviation.…”

Section: Methodsmentioning

confidence: 99%

“…Importantly, chaotic systems are able to produce an infinite number of dynamic behaviors, both periodic and nonperiodic, in nature (36). A common feature of determinism is that one state of the system is similar to a previous state, and this can be measured mathematically by using a number of tests, including recurrence plots (37). Analysis revealed recurrent behavior, suggestive of determinism, in Nod factor-induced calcium spiking and to a lesser extent in mycorrhizal-induced calcium changes (Fig.…”

Section: Rhizobial Bacteria and Mycorrhizal Fungi Induce Differentialmentioning

confidence: 99%

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Differential and chaotic calcium signatures in the symbiosis signaling pathway of legumes

Kosuta

Hazledine²,

Sun³

et al. 2008

Proc. Natl. Acad. Sci. U.S.A.

252

215

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Understanding how the cell uses a limited set of proteins to transduce very different signals into specific cellular responses is a central goal of cell biology and signal transduction disciplines. Although multifunctionality in signal transduction is widespread, the mechanisms that allow differential modes of signaling in multifunctional signaling pathways are not well defined. In legume plants, a common symbiosis signaling pathway composed of at least seven proteins mediates infection by both mycorrhizal fungi and rhizobial bacteria. Here we show that the symbiosis signaling pathway in legumes differentially transduces both bacterial and fungal signals (inputs) to generate alternative calcium responses (outputs). We show that these differential calcium responses are dependent on the same proteins, DMI1 and DMI2, for their activation, indicating an inherent flexibility in this signaling pathway. By using Lyapunov and other mathematical analyses, we discovered that both bacterial-induced and fungalinduced calcium responses are chaotic in nature. Chaotic systems require minimal energy to produce a wide spectrum of outputs in response to marginally different inputs. The flexibility provided by chaotic systems is consistent with the need to transduce two different signals, one from rhizobial bacteria and one from mycorrhizal fungi, by using common components of a single signaling pathway.chaos ͉ mycorrhization ͉ nodulation

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Section: Rhizobial Bacteria and Mycorrhizal Fungi Induce Differentialmentioning

confidence: 67%

Section: Methodsmentioning

confidence: 99%

Section: Rhizobial Bacteria and Mycorrhizal Fungi Induce Differentialmentioning

confidence: 99%

See 1 more Smart Citation

Differential and chaotic calcium signatures in the symbiosis signaling pathway of legumes

Kosuta

Hazledine²,

Sun³

et al. 2008

Proc. Natl. Acad. Sci. U.S.A.

252

215

View full text Add to dashboard Cite

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“…In Figure 6, more of the recurrence points are observed in the main diagonal lines for these time series, while the recurrence structure consisting of roughly vertical (horizontal) patterns can be found in the plots of Figure 7. Since the graphical representation may be difficult to evaluate, recurrence quantification analysis (RQA) [41,42,49] was developed to provide numerical measures that allow for the quantification of the structure and complexity of RPs. These quantities are based on recurrence points densities, diagonal and vertical line structure.…”

Section: Recurrence Plot and Recurrence Quantification Analysismentioning

confidence: 99%

“…Furthermore, nonlinear determinism can potentially explain large movements in financial data that linear stochastic models cannot account for [38]. Thus, we here apply the recurrence plots (which provide visual insight into the complex nonlinear deterministic patterns in time series data [39,40]) and the recurrence quantification analysis (RQA) method (that is able to quantify structure in the recurrence plots through different recurrence measures [41,42]) to the nonlinear analysis of the real market data and the simulated data derived from the financial price model.…”

Section: Introductionmentioning

confidence: 99%

Entropy and Recurrence Measures of a Financial Dynamic System by an Interacting Voter System

Niu

Wang

2015

Entropy

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A financial time series agent-based model is reproduced and investigated by the statistical physics system, the finite-range interacting voter system. The voter system originally describes the collective behavior of voters who constantly update their positions on a particular topic, which is a continuous-time Markov process. In the proposed model, the fluctuations of stock price changes are attributed to the market information interaction amongst the traders and certain similarities of investors' behaviors. Further, the complexity of return series of the financial model is studied in comparison with two real stock indexes, the Shanghai Stock Exchange Composite Index and the Hang Seng Index, by composite multiscale entropy analysis and recurrence analysis. The empirical research shows that the simulation data for the proposed model could grasp some natural features of actual markets to some extent.

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An Introduction to Dynamical Systems Theory

Sujith

Pawar

2021

Springer Series in Synergetics

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As we discussed in Chap. 1, the onset of thermoacoustic instability is a nonlinear phenomenon resulting from the coupled interaction between the acoustic field in a combustor and the heat release rate field of the flame. A thermoacoustic system can undergo different dynamical transitions (called bifurcations), due to a change in any system (control) parameter. We observe that the characteristics of such dynamical transitions are governed primarily by the type of the underlying flow field, i.e., laminar or turbulent flows, present in a combustor. As a result, we notice the occurrence of different dynamical states during the onset of thermoacoustic instability in laminar and turbulent thermoacoustic systems. Furthermore, tools based on linear time series analysis are not sufficient to reveal many features exhibited by nonlinear thermoacoustic systems. In order to overcome the limitations of linear approaches in analyzing the data from experiments or numerical simulations, we need different methodologies based on dynamical systems theory to accurately characterize the nonlinear behaviors of thermoacoustic systems. In this chapter, we will introduce the basics of dynamical systems theory and cover different topics such as stability analysis, bifurcations, attractors, nonlinear measures, phase space reconstruction, Poincaré section, and recurrence plot. In the subsequent chapters, we will explore the application of these methodologies to perform time series analysis of the data obtained from experiments and numerical simulations performed on both laminar and turbulent thermoacoustic systems. Dynamical SystemThe properties of most natural and man-made systems vary with time. Some examples include the displacement of a swinging pendulum, the growth of a particular species in forest, the temperature of the earth's surface in a day, heartbeats, the local velocity of a turbulent flow, etc. A system whose behavior changes as

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Detecting determinism using recurrence quantification analysis: Three test procedures

Cited by 34 publications

References 21 publications

Differential and chaotic calcium signatures in the symbiosis signaling pathway of legumes

Differential and chaotic calcium signatures in the symbiosis signaling pathway of legumes

Entropy and Recurrence Measures of a Financial Dynamic System by an Interacting Voter System

An Introduction to Dynamical Systems Theory

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