Dynamical characteristics of magnetospheric energetic ion time series: evidence for low dimensional chaos

Athanasiu, M. A.; Pavlos, G. P.; Sarafopoulos, D. V.; Sarris, E. T.

doi:10.5194/angeo-21-1995-2003

Cited by 8 publications

(7 citation statements)

References 65 publications

(41 reference statements)

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“… Chian et al [2000] and Chian et al [2002c] showed that chaos can appear in a three‐wave model of magnetospheric radio emissions involving nonlinear interactions of Langmuir, whistler, and Alfvén waves in the auroral acceleration regions, which can generate type‐I intermittency and crisis‐induced intermittency in auroral plasmas. Athanasiu et al [2003] obtained evidence of chaos in the time series of energetic magnetospheric ions based on the Lyapunov spectrum, mutual information and prediction models. Kuo et al [2004] studied the chaotic behavior of the trajectories of trapped relativistic electrons interacting with large‐amplitude whistler waves in the magnetosphere; a surface of section technique was used to examine the system chaoticity graphically.…”

Section: Discussionmentioning

confidence: 99%

On the chaotic nature of solar‐terrestrial environment: Interplanetary Alfvén intermittency

et al. 2006

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[1] We present an overview of observational and theoretical evidence of chaos and intermittency in the solar-terrestrial environment including solar dynamo, solar atmosphere, solar wind, and terrestrial magnetosphere-ionosphere-atmosphere. The chaotic nature of space plasmas is studied by a nonlinear model of Alfvén waves described by the low-dimensional limit of the derivative nonlinear Schrödinger equation given by its stationary solutions in the frame moving with the driver wave velocity. A periodic window of the bifurcation diagram is constructed to identify two types of Alfvén chaos related to type-I intermittency and crisis-induced intermittency. We show that an Alfvén chaotic attractor is composed of chaotic saddles and unstable periodic orbits and explain the links between these unstable structures and Alfvén intermittency. The role of interplanetary Alfvén intermittency in the solar wind driving of intense geomagnetic activities is discussed.

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Section: Discussionmentioning

confidence: 99%

On the chaotic nature of solar‐terrestrial environment: Interplanetary Alfvén intermittency

et al. 2006

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“…where { e i j } new set of orthogonal vectors produced by orthonormalisation of the vectors at time i in order to retain the local orthogonal spanning of the state space (Athanasiu et al, 2003). Another significant quantifier used in chaotic analysis is the correlation dimension, D which is defined as:…”

Section: Time Series and Phase Spacementioning

confidence: 99%

A comparative study on chaoticity of equatorial/low latitude ionosphere over Indian subcontinent during geomagnetically quiet and disturbed periods

Unnikrishnan

2010

Nonlin. Processes Geophys.

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Abstract. In the present study, the latitudinal aspect of chaotic behaviour of ionosphere during quiet and storm periods are analyzed and compared by using GPS TEC time series measured at equatorial trough, crest and outside crest stations over Indian subcontinent, by employing the chaotic quantifiers like Lyapunov exponent (LE), correlation dimension (CD), entropy and nonlinear prediction error (NPE). It is observed that the values of LE are low for storm periods compared to those of quiet periods for all the stations considered here. The lowest value of LE is observed at the trough station, Agatti (2.38 • N, Geomagnetically), and highest at crest station, Mumbai (10.09 • N, Geomagnetically) for both quiet and storm periods. The values of correlation dimension computed for TEC time series are in the range 2.23-2.74 for quiet period, which indicate that equatorial ionosphere may be described with three variables during quiet period. But the crest station Mumbai shows a higher value of CD (3.373) during storm time, which asserts that four variables are necessary to describe the system during storm period. The values of non linear prediction error (NPE) are lower for Agatti (2.38 • N, Geomagnetically) and Jodhpur (18.3 • N, Geomagnetically), during storm period, compared to those of quiet period, mainly because of the predominance of non linear aspects during storm periods The surrogate data test is carried out and on the basis of the significance of difference of the original data and surrogates for various aspects, the surrogate data test rejects the null hypothesis that the time series of TEC during storm and quiet times represent a linear stochastic process. It is also observed that using state space model, detrended TEC can be predicted, Correspondence to: K. Unnikrishnan (kaleekkalunni@gmail.com) which reasonably reproduces the observed data. Based on the values of the above quantifiers, the features of chaotic behaviour of equatorial trough crest and outside the crest regions of ionosphere during geomagnetically quiet and disturbed periods are briefly discussed.

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“…One approach to giving more equal weight to errors across several orders of magnitude is to use metrics that are based on relative errors (Subbotin & Shprits, 2009;Zhelavskaya et al, 2016) or are otherwise scaled to normalize the errors (Athanasiu et al, 2003;Welling, 2010). Alternatively, the data themselves can be transformed through the application of a power function, such as taking logarithms or applying a Box-Cox transform (Wilks, 2006).…”

Section: 1002/2017sw001669mentioning

confidence: 99%

Measures of Model Performance Based On the Log Accuracy Ratio

2018

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Quantitative assessment of modeling and forecasting of continuous quantities uses a variety of approaches. We review existing literature describing metrics for forecast accuracy and bias, concentrating on those based on relative errors and percentage errors. Of these accuracy metrics, the mean absolute percentage error (MAPE) is one of the most common across many fields and has been widely applied in recent space science literature and we highlight the benefits and drawbacks of MAPE and proposed alternatives. We then introduce the log accuracy ratio and derive from it two metrics: the median symmetric accuracy and the symmetric signed percentage bias. Robust methods for estimating the spread of a multiplicative linear model using the log accuracy ratio are also presented. The developed metrics are shown to be easy to interpret, robust, and to mitigate the key drawbacks of their more widely used counterparts based on relative errors and percentage errors. Their use is illustrated with radiation belt electron flux modeling examples.

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Dynamical characteristics of magnetospheric energetic ion time series: evidence for low dimensional chaos

Cited by 8 publications

References 65 publications

On the chaotic nature of solar‐terrestrial environment: Interplanetary Alfvén intermittency

On the chaotic nature of solar‐terrestrial environment: Interplanetary Alfvén intermittency

A comparative study on chaoticity of equatorial/low latitude ionosphere over Indian subcontinent during geomagnetically quiet and disturbed periods

Measures of Model Performance Based On the Log Accuracy Ratio

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