Dynamical Complexity Transitions During High‐Intensity Long Duration Continuous Auroral Activities (HILDCAA) Events: Feature Analysis Based on Neural Network Entropy

In this study, we examine the dynamical complexity transitions during HILDCAA events. HILDCAA preceded by an Interplanetary Coronal Mass Ejection (ICME) storm recovery phase, HILDCAA preceded by a Corotating Interaction Region (CIR) storm recovery phase, and non‐storm driven HILDCAA and geomagnetically quiet periods were investigated using the Auroral Electrojet index time series. Neural Network Entropy (NNetEn) was used to capture the dynamical complexity transitions during these sporadic events. The NNetEn was able to decipher the distinct dynamical features associated with the emergence of HILDCAA and the geomagnetically quiet periods. Our analysis revealed a high value of NNetEn during HILDCAA signifying that the complexity levels of the coupled solar wind‐magnetosphere‐ionosphere system for HILDCAA, driven by different interplanetary structures were high with no significance difference. Thus, indicating that during HILDCAA, the dynamical behavior of the underlying physical processes due to the energy deposition driven either by ICME, CIR or non‐storm HILDCAA remain the same. However, a deciphering feature of dynamical complexity between the geomagnetically quiet period and HILDCAA events was evident. It was noticed that as the HILDCAA emerges, the NNetEn depicts an increment in entropy value signifying that the complexity levels of the coupled solar wind‐magnetosphere‐ionosphere system increases, and as the dynamics transcend to its recovery state, a reduction in entropy was observed implying a decline in complexity levels. Low values of NNetEn revealing lower complexity levels are found to be associated with geomagnetically quiet periods.


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2 of 14 from the coronal hole in the form of High-Speed solar wind streams.They are elastic transverse waves that travel along the magnetic field lines with magnetic tension as the restoring force (Guo et al., 2016).When these Alfvénic waves collide with the dynamics of the magnetosphere, magnetic reconnection between the intermittent southward magnetic field of Alfvén waves and the magnetopause magnetic field occurs, leading to HILD-CAA (Kim, 2007;Prestes et al., 2017;Vega & Favetto, 2000).Another prominent mechanism that can drive the occurrence of HILDCAA is the process of Kelvin-Helmholtz viscous interaction.The process involves plasma transport at the magnetospheric boundaries driven by plasma corotation, kinetic effects, and asymmetric plasma distribution (Chen et al., 1997;Hwang et al., 2022;Palermo, 2019).
One of the features of the geospace environment attributed to the HILDCAA event is the associated aurora displayed.It is reported that aurora exhibited during HILDCAA is differs from aurora display during geomagnetic storms.For instance, during HILDCAA, the Auroras are distributed in the whole auroral oval covering all local times and last several days, while during geomagnetic storms, auroral are confined in small regions and last for few days or minutes (Guarnieri et al., 2006).Interestingly, the underlying physical processes of the AE signatures as HILDCAA emerges are connected with long-duration of large amplitude Alfvénic fluctuations, which possess some inherent irregularities in its underlying dynamics.Its influence on the internal dynamics of the magnetosphere would lead to chaotic variation due to the inherent irregularities driven by magnetic reconnections and viscous interactions (Alberti et al., 2020(Alberti et al., , 2022;;Balasis et al., 2009Balasis et al., , 2023;;Consolini, 2018;Donner et al., 2019;Manshour et al., 2021;Mendes et al., 2017;Ogunsua, 2018;Oludehinwa, Olusola, Bolaji, & Odeyemi, 2021;Oludehinwa, Olusola, Bolaji, Odeyemi, & Njah, 2021;Pavlos, 1994;Pavlos et al., 1992Pavlos et al., , 1999;;Toledo et al., 2021).It is well established that the Earth's magnetosphere is driven by the solar wind and exhibits complex dynamical features especially during severe space weather conditions.Its dynamics is essentially determined by the interaction between its components and the characteristic of its drivers with the solar wind plasma.The underlying cause of this complex dynamics of the coupled solar wind-magnetosphere-ionosphere system is the inherent nonlinearity of the magnetospheric plasma and the turbulent nature of the solar wind.Furthermore, the coupled solar wind-magnetosphere-ionosphere as a dynamical system is far from equilibrium.Therefore, the emergence of a non-equilibrium characteristics exhibits a certain degree of spatio-temporally coherent features resulting from the multiple interaction among elementary parts, called dynamical complexity (Coco et al., 2011;Consolini, 2018).Chang et al. (2006) explained dynamical complexity as a phenomenon exhibited by a nonlinear interacting dynamical system within which multitudes of different sizes of large-scale coherent structures are formed, resulting in a global nonlinear stochastic behavior for the dynamical system.The term dynamical complexity is used to describe the complexity of a dynamical system, that is, the coupled solar wind-magnetosphere-ionosphere system for HILDCAA and reveals information about the complexity level of such system (i.e., higher entropy means higher complexity or less order for the system under study, while lower entropy translates to lower complexity or higher order for the system under study).
With the development of Artificial Intelligence applications in monitoring the space weather conditions to alert and mitigate the effect of this phenomenon on spacecraft technology.There is a need to extract some nonlinear dynamical information associated with this sporadic event using the concept of information theory because the spatial structures of the AE signatures as HILDCAA emerges is the next key issue that would enable further understanding of the coupled solar wind-magnetosphere-ionosphere system which is also a prerequisite to developing the capability to make regional forecast of space weather conditions and recognizing the nonlinear nature of the magnetosphere and its evident complexity attributed to HILDCAA.The HILDCAA is identified when the Auroral electrojet (AE) index peaks at least 1,000 nT and does not drop below 200 nT for more than 2 hr.In addition, the features will last for a long-duration (minimum of 2 days) and occur outside the main phase of geomagnetic storm (Tsurutani & Gonazalez, 1987;Tsurutani et al., 2004).One of the space weather consequences associated with the emergence of HILDCAA events is the emanation of killer electrons (i.e., electrons trapped in Earth's outer radiation belt) that can cause significant hazards on spacecraft technology systems such as Navigation, Communication, and weather monitoring satellites (Hajra et al., 2015).
Several authors have established some findings about the solar wind-magnetosphere-ionosphere coupling processes during HILDCAAs events (Chernyshov et al., 2020;Guarnieri, 2006;Hajra et al., 2013;Marques de Souza Franco et al., 2019;Obara et al., 2000;Prestes et al., 2017;Silva et al., 2017;Sobral et al., 2006;Tsurutani et al., 1990Tsurutani et al., , 2004Tsurutani et al., , 2005)).The investigation carried out by Vega and Favetto (2000) reported the magnetosphere's response to perturbation by storms and Alfvén waves train.The authors used correlation dimension and surrogated data set method to unveil the features of HILDCAA and found that the case corresponding to the OLUDEHINWA ET AL.
10.1029/2023SW003475 3 of 14 HILDCAA event was the most predictable with the assertion that the magnetosphere acts as a stationary excited system.Hajra et al. (2015) investigate the HILDCAA events of isolated and those occurring in the recovery phase of geomagnetic storms induced by Corotating Interaction Regions (CIRs).They found that CIR magnetic storms followed by HILDCAA events depicts almost identical relativistic electron signatures.The isolated events are found to be comparatively weaker and shorter than the storm-related events.Mendes et al. (2017) applied the recurrence quantification analysis (RQA) to reveal the dynamical behavior during HILDCAA.They reported that the RQA indicate clearly the dynamics associated with quiet intervals and HILDCAA.Adhikari et al. (2018) studied the interplanetary parameters, polar cap potential, and polar cap index during geomagnetical quiet periods and HILDCAA events.Little perturbations in interplanetary electric field were found at geomagnetic quiet event, while during HILDCAA, significant perturbation was noticed.Marques de souza et al. ( 2019) examined the magnetotail responses to the solar wind during HILDCAA events using wavelet transform analysis.The authors identified the most energetic period (76% of HILDCAA have periods less equal to 4 hr).In addition, they reported that the magnetotail responds to IMF fluctuations during HILDCAA.Rout et al. (2022) used the wavelet transform and cross-spectrum analysis to examine the responses of two HILDCAA events to solar wind observation.It was found that the quasi-periodic oscillation of 1.5-2 hr in the interplanetary electric field is the most effective parameter that controls the solar wind-magnetosphere-Ionosphere coupling process during HILDCAA events.
Despite the considerable body of knowledge outlined in the above literature and reference therein, the dynamical behavior of HILDCAA have not been examined from the concept of information theory.The spatial and temporal scales in amplitude changes of Auroral Electrojet (AE) wave patterns are associated with the coupled solar wind-magnetospheric-ionospheric responses to the external influences emanating from the sun, which are propagated nonlinearly.This nonlinearity would have great influence on the complexity and internal dynamics of the magnetosphere-ionosphere coupling since all these inherent irregularities can lead to chaotic variation at all geophysical condition (Tsurutani et al., 1990(Tsurutani et al., , 2005;;Unnikrishnan & Ravindran, 2010).Notably, the dynamical behavior of the AE fluctuation signatures associated with the emergence of HILDCAA can be captured through the concept of information theory.This prompted the idea to use Neural Network Entropy (NNetEn) to unveil the dynamical complexity transitions in the dynamics of the coupled solar wind-magnetosphere-ionosphere system as HILDCAA emerges and as it transcends to a recovery state.In nonlinear dynamics, the concept of entropy is developed from information theory to measure the degree of complexity in a dynamical system.NNetEn is an artificial intelligence developed from information theory, and applies LogNNet model (Velichko, 2020;Velichko & Heidari, 2021;Velichko, Belyaev, et al., 2022;Velichko, Wagner, et al., 2022).The model calculates entropy directly without considering or approximating probability distributions.NNetEn has proven to be a valuable tool for studying the dynamical complexity of a system (Oludehinwa et al., 2022;Velichko, Belyaev, et al., 2022;Velichko, Wagner, et al., 2022;Velichko et al., 2023).
Our research question addresses how the complexity levels respond as HILDCAA emerges, and as it transcends to the recovery state with the goal of using the NNetEn.So that, the dynamical information that are associated with the HILDCAA events can be unveiled.Furthermore, to unveil to the space science community the potential of the NNetEn as a diagnostic tool to capture the dynamical information associated with space weather conditions.Therefore, in this study, we carried out a detailed analysis of dynamical complexity transition during HILDCAA events.By investigating the dynamical behavior of the HILDCAA event preceded by different interplanetary structures.The information obtained will be additional information in understanding the space weather conditions during HILDCAA, especially from its ascending and recovery state.In Section 2, our method of data acquisition is described and the NNetEn that we employed in this work is explained in detailed.In Section 3, we present the results and discussion and the conclusion is drawn in Section 4.

Data Acquisition and Method of Analysis
To analyze the dynamical behavior of the HILDCAA events preceded by different interplanetary structures shown in Table 1, we used a high-resolution 1-min Auroral Electrojet index data.The AE index is produced by the World Data Center, Kyoto, Japan (https://wdc.kugi.kyoto-u.ac.jp/index.html).However, the AE index data was obtained from the online database of space Physics facility, NASA (https://omniweb.gsfc.nasa.gov/form/omni_min.html).The criteria for identifying these sporadic events according to the work of Tsurutani and Gonazalez (1987) was considered such that, the AE signal peaks to at least 1,000 nT once during the event and does not drop below 200 nT for more than 2 hours at a time.The feature last for at least 2 days and occur outside the main phase of geomagnetic storm.Five HILDCAA events each, HILDCAA preceded by an Interplanetary Coronal Mass Ejection (ICME) storm recovery phase, HILDCAA by a CIR storm recovery phase, and non-storm driven HILDCAA were selected and geomagnetically quiet periods.The selected events were in accordance to the study of Khanal et al. (2019) that separated the HILDCAA based on their interplanetary drivers.Furthermore, we also considered events whose AE index depicts from the ascending of HILDCAA to the emergence of HILD-CAA and transcend to its recovery state, so that the transition features of dynamical complexity behavior can be unveiled from ascending and recovery period to HILDCAA period.

Calculation of Neural Network Entropy Measures
NNetEn is an artificial neural network LogNNet model developed by Velichko and Heidari (2021) to quantify the degree of complexity in a dynamical system.An implementation of the algorithms in Python is presented in Velichko et al., 2023 and package for NNetEn calculation involved in this study is publicly available on GitHub.The model is based on classification accuracy and computes entropy directly without considering the concept of probability distribution.Its algorithm modifies the structure of the LogNNet classification model such that the classification accuracy of the MNIST-10-digit data set indicates the complexity of a given time series (Velichko, 2020;Velichko, Belyaev, et al., 2022;Velichko, Wagner, et al., 2022).The MNIST data set contains handwritten numbers from "0" to "9" with 60,000 training and 10,000 testing.NNetEn model structure for calculating the entropy comprises the input layer, a reservoir model of the matrix (W 1 ) to transform input vector (Y) into another vector (S h ), and a single-layer feed-forward neural network transforming vector (S h ) into digits 0-9 in the output layer (S out ) shown in Figure 1.The NNetEn algorithm estimates the entropy in the following stages: the stage 1 involves loading the time series X = (x 1 , x 2 , x 3 , … , x N ) into the reservoir.In the reservoir, transformation of the input vector (Y) through a time series (X) is achieved by filling the matrix of the reservoir with the time series using row-wise filling time series stretching, method 3 (Heidari et al., 2023) Where E p is the number of epochs used in calculating the entropy.The number of epochs (E p ) used in calculating the entropy is 20.The final list of parameters for calculating NNetEn using the Python module: database = "D1", mu = 1, epoch = 20, method = 3, and metric = "Acc".
In this study, we propose a signal preprocessing through which the value of the constant offset (B) is subtracted from the AE time series data.
Where  AE is the Auroral Electrojet time series while  AE ′  is the modified Auroral Electrojet time series and B is the constant offset value, also known as bias component.Interested readers are referred to the work of Heidari et al. (2023) where a detailed description of constant offset, B, is given.The offset value is estimated by averaging all the AE index time series investigated  ( = 370) .Then a signal preprocessing is applied to the AE index using Equation 2. To calculate the dynamical complexity transition.A local and global method of entropy was used, which involves a local series of the same interval  (NL) and step (S).The principle is based on splitting the time series

𝐴𝐴
NNetEn local entropy enable one to capture the changes in entropy along the entire series of the event.Hence, trace the transition features of the complexity levels as HILDCAA emerges.Furthermore, the method allows one to define the global entropy  (GNNetEn) as the average value of all the local entropy  NNetEn .

Results and Discussion
The spatial and temporal scales in amplitude changes of Auroral Electrojet wave patterns are associated with the coupled solar wind-magnetosphere-ionosphere responses to the external influences emanating from the sun and the internal processes prompting the emergence of complex dynamics in its underlying physical process.OLUDEHINWA ET AL.

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6 of 14 In the study, we apply the concept of Neural Network Entropy using local and global approach which involves calculating the entropy from a local series of the same length (NL) and step (S) to capture the dynamical complexity transitions during HILDCAA events.Figures 3a-3c show the changes in NNetEn during 11-19 October 1992 HILDCAA event preceded by CIR storm recovery phase.Figure 3a  In Figures 4a and 4b, we present a bar chart of global entropy (GNNetEn) for HILDCAA preceded by a CIR storm recovery phase, HILDCAA preceded by an ICME storm recovery phase, non-storm driven HILDCAA and geomagnetically quiet periods.The bar chart revealed a clear distinct between the HILDCAA driven by different interplanetary structures and the geomagnetically quiet periods.Statistically, at NL = 200 (short interval of splitting), B = 370 shown in Figure 4a, the threshold value of GNNetEn for HILDCAA events is 0.494 while at geomagnetically quiet periods, the threshold value of GNNetEn is 0.246.For NL = 2,000 (long interval of splitting), B = 370 display in Figure 4b, the threshold value of GNNetEn during HILDCAA is 0.669 and the geomagnetically quiet periods is 0.396.However, the values of GNNetEn for HILDCAA preceded by CIR storm recovery phase, HILDCAA preceded by ICME storm recovery phase and non-storm driven HILDCAA are high with no significant difference in entropy.The observation of high GNNetEn values during HILDCAA preceded by different interplanetary structures indicates that the complexity levels of the coupled solar wind-magnetosphere-ionosphere system is high as HILDCAA emerges.It further implies that irrespective of the interplanetary structures driving the emergence of HILDCAA, the dynamical behavior of the physical processes remains the same.Interestingly, it is worthy to note that there is a distinct dynamical behavior associated with the emergence of HILD-CAA and the geomagnetically quiet periods.
Figures 5a and 5b shows the transition features of NNetEn changes as HILDCAA emerges and as it transcends to its recovery periods on 20-26 August 2006.In Figure 5a depicting the signal of the AE index time series during HILDCAA from 20-26 August 2006.We noticed that the time series of the AE index from n = 0-4,900 min exhibits the features of HILDCAA emergence while from n = 5,000-10,000 depicts its recovery features where the signal of the AE index exhibits weak fluctuation signatures.Figure 5b displays the NNetEn transition features associated with these periods.An enhancement in NNetEn is found to be associated with the emergence of HILDCAA, while a decline in NNetEn begins to unveil as the HILDCAA tends toward the recovery periods.The transition mode of NNetEn (T tr = 4,150) minutes indicated in Figure 5b present the transition time when the enhancement in dynamical complexity behavior due HILDCAA emergence begins to decline.This observation strengthened the evidence that as HILDCAA emerges, the complexity levels of the coupled solar wind-magnetosphere-ionosphere system increases, while as the HILDCAA transcend to its recovery periods, the complexity levels decreases.Figures 6a and 6b is the AE signal depicting the emergence of HILDCAA with its It was noticed that the changes in NNetEn depict high entropy during the emergence of HILDCAA which is obvious at n = 0-7,000 min while low entropy was observed as the AE signal transcend to its recovery period.This low entropy observed as HILDCAA transcend to it recovery state signifies a reduction in dynamical complexity.This observed feature may be attributed to less activities of irregularities in the underlying dynamics of the coupled solar wind-magnetosphere-ionosphere system due to particle injection that usually occur at the polar region.Alberti et al. (2020) reported a scale-dependent dynamical transitions  We noticed that the signal of the AE index within n = 0-2,500 min and 20,000-250,000 min exhibit a weak fluctuation signature (i.e., associated with ascending and recovery period of HILDCAA).During these ascending  See Table 2, where the values of global entropy (GNNetEn) at before, during, and after HILDCAA occurrence was computed to further validate our findings.This enhancement in complexity levels during the emergence of HILDCAA may be attributed to the elongated particle injection of solar wind energy into the dynamics of the magnetosphere that generally occur in the polar regions (Hajra & Tsurutani, 2018;Hajra et al., 2020;Tsurutani et al., 2009Tsurutani et al., , 2020)).
Figures 10a and 10b shows the NNetEn transition features during geomagnetically quiet period on 19-25 June 2004.The column in Figure 10a depicts the time series of the AE index during geomagnetically quiet period.The column in Figure 10b represents the changes in NNetEn during the geomagnetically quiet period on 19-25 June 2004.The changes in NNetEn at NL = 2,000 is indicated in black color while the NNetEn changes at NL = 200 is indicated in blue color.It was noticed that NNetEn transient features during this geomagnetically quiet period depicts a decline in entropy throughout the entire series.Inaddition, it was further noticed that the trend in NNetEn changes for NL = 200 and 2,000 did not reach up to 0.6 compared to the period of HILDCAA events investigated.This observation indicates that there is decline in dynamical complexity behavior during geomagnetically quiet periods.Similar features of NNetEn changes were also noticed on 23-27 May 2005 a day of geomagnetically periods shown in Figure 11.It was also observed that there is decline in NNetEn changes during this period, which further strengthened the evidence that lower complexity levels are associated with geomagnetically quiet periods.For the first time and as far as we know, this work had shown that as HILDCAA emerges, the complexity levels of the coupled solar wind-magnetosphere-ionosphere system increases and as it transcends to recovery state, the levels of complexity decreases.This dynamical information can be a useful diagnosis in monitoring the activities of  HILDCAA events through Neural Network Entropy (NNetEn).Furthermore, the spatial structures of the AE signatures during HILDCAA is the next key issue that would enable further understanding of the magnetospheric dynamics associated with HILDCAA which is also a prerequisite to developing the capability to make regional forecast of space weather condition and recognizing the nonlinear nature of the magnetosphere and its evident complexity attributed to HILDCAA.Notably, the observation of dynamical complexity during geomagnetic storms and substorms activity have been well reported by several authors.For instance, Balasis et al. (2006Balasis et al. ( , 2008Balasis et al. ( , 2009)), Oludehinwa, Olusola, Bolaji, and Odeyemi (2021), and Oludehinwa, Olusola, Bolaji, Odeyemi, & Njah (2021) found lower entropy/lower complexity around intense magnetic storms, while Michelis and Consolini (2015) found higher entropy/higher complexity around magnetospheric substorms similar to the results presented herein for HILDCAA.So, substorm events and HILDCAA events seem to follow a very similar dynamical behavior.

Conclusion
This work had examined the dynamical complexity transitions during HILDCAAs events.HILDCAA events preceded by an ICME storm recovery phase, HILDCAA preceded by a CIR storm recovery phase, non-storm driven HILDCAA and geomagnetically quiet period were investigated.Neural Network Entropy (NNetEn) was used to capture the dynamical complexity transitions during these sporadic events.The NNetEn was able to decipher the distinct dynamical features associated with the emergence of HILDCAA and geomagnetically quiet periods.Our analysis revealed that the NNetEn depicts high values of entropy signifying that the complexity levels of the coupled solar wind-magnetosphere-ionosphere system for HILDCAA preceding different interplanetary structures (ICME preceded HILDCAA, CIR preceded HILDCAA and non-storm driven HILDCAA) are high with no significance difference between them.A common observation for all the characteristics HILDCAA events is that the dynamical complexity is higher.Thus, indicating that during HILDCAA, the underlying physical processes of magnetospheric dynamics remain the same, irrespective of the interplanetary structures driving the event.However, a deciphering feature of dynamical complexity behavior between the geomagnetically quiet and HILDCAA events was evident.It was noticed that as HILDCAA emerges, high values of NNetEn were observed indicating that the complexity levels increases as HILDCAA emerges while a reduction in NNetEn was observed as the dynamics transcend to its recovery state implying a decline in complexity levels of the coupled solar wind-magnetosphere-ionosphere system.

Figure 1 .
Figure 1.The structure of LogNNet Model of Neural Network Entropy.
6, the vector (S h ) enters the input layer of the classifier with a dimension of P max = 25.Stage 7, the vector (S h ) undergoes the normalization process.Stage 8, involves a single-layer output with 10 neutrons for MNIST data set.Stages 9-10, the training and testing process of the neutral network is performed and the classification accuracy is determined.Stage 11: NNetEn is then calculated.NNetEn is computed using the following expression.NNetEn() =classif ication accurracy 100%

Figure 2 .
Figure 2. Illustrates the splitting of the  AE ′  index time series into equal interval (NL) and Step (S).
represents the result of the NNetEn at NL = 200 (short interval of splitting), B = 370 and Figure3bdepicts the NNetEn changes at NL = 2,000 (long interval of splitting), B = 370.Figure3cis the time series of the AE index depicting the HILDCAA features.A decline in NNetEn changes was observed at the regions where the fluctuation signatures of the AE signal is weak.For instance, in Figure3aat n = 3,000-4,000 min, the wave pattern of the AE signal is noticed to be characterized by a weak fluctuation signatures and the NNetEn depicts a reduction in entropy changes.At n = 6,000-8,000 min, the wave pattern of the AE signal is noticed to be characterized by a strong fluctuation signatures and the NNetEn depicts an increment in entropy changes.Inaddition, it was noticed that the values of the global entropy (GNNetEn) estimated from the changes in NNetEn for B = 370, NL = 200 is 0.473 while B = 370, NL = 2,000 is 0.663.This observation implies that the NNetEn calculation at B = 370, NL = 200 and B = 370, NL = 2,000 shown in Figure3gives a better approach in capturing the transient features of dynamical complexity during HILDCAA event.

Figure 3 .
Figure 3. (a-c): Show the changes in Neural Network Entropy (NNetEn) transition for 11-19 October 1992 HILDCAA preceded by Corotating Interaction Region storm recovery phase.At NL = 200 with three option of offset value (b).The column (a) is the NNetEn and the GNNetEn for B = 370, NL = 200 (Short interval of splitting); (b) is the NNetEn and GNNetEn for B = 370, NL = 2,000 (Long interval of splitting); (c) is the AE time series depicting the signatures of HILDCAA on 11-19 October 1992.

Figure 4 .
Figure 4. (a and b): Show the GNNetEn for HILDCAA preceded by a Corotating Interaction Region, HILDCAA preceded by a Interplanetary Coronal Mass Ejection, nonstorm driven HILDCAA and geomagnetically quiet periods.

Figure 5 .
Figure 5.The Neural Network Entropy transition features as HILDCAA emergences and its transcending to recovery state on 20-26 August 2006 at NL = 2,000 (shown in black color), NL = 200 (shown in blue color).Transition time (T tr ) between HILDCAA and recovery period is 4,150 min.

Figure 6 .
Figure 6.The Neural Network Entropy transition features as HILDCAA emergences and its transcending to recovery state on 3-10 July 2003 at NL = 2,000 (shown in black color), NL = 200 (shown in blue color).Transition time (T tr ) between HILDCAA and recovery period is 2,300 min.

Figure 7 .
Figure 7.The Neural Network Entropy transition features as HILDCAA emergences and its transcending to recovery state on 21-27 May 2005 at NL = 2,000 (shown in black color), NL = 200 (shown in blue color).Transition time (T tr ) between HILDCAA and recovery period is 4,690 min.

Figure 8 .
Figure 8.The Neural Network Entropy transition features from its ascending state to the emergence of HILDCAA and finally to its recovery state on 18 November-5 December 2004 at NL = 2,000 (shown in black color), NL = 200 (shown in blue color).Transition time (T tr ) between HILDCAA and recovery period is 4,600 min.

Figure 9 .
Figure 9.The Neural Network Entropy transition features from its ascending state to the emergence of HILDCAA and finally to its recovery state on 10-23 October 2003 at NL = 2,000 (shown in black color), NL = 200 (shown in blue color).Transition time (T tr ) between HILDCAA and recovery period is 2,900 min.

Figure 10 .
Figure 10.The Neural Network Entropy (NNetEn) transition features during geomagnetically quiet period on 19-25 June 2004.The column in 10(a) depicts the time series of the AE index during geomagnetically quiet period.Column 10(b) is the changes in NNetEn during the geomagnetically quiet period on 19-25 June 2004.

Figure 11 .
Figure 11.The Neural Network Entropy (NNetEn) transition features during geomagnetically quiet period on 23-27 May 2005.The column in 10(a) depicts the time series of the AE index during geomagnetically quiet period.Column 10(b) is the changes in NNetEn during the geomagnetically quiet period on 23-27 May 2005.

Table 1
The List of HILDCAA Events Preceded by Different Interplanetary Structure and Geomagnetically Quiet Period Investigated in This Study Transition time (T tr ) between HILDCAA and recovery period is 2,900 min.