Comparison of chaotic aspects of magnetosphere under various physical conditions using AE index time series

Abstract

Abstract. The deterministic chaotic behaviour of magnetosphere was analyzed, using AE index time series. The significant chaotic quantifiers like, Lyapunov exponent, spatiotemporal entropy and nonlinear prediction error for AE index time series under various physical conditions were estimated and compared. During high solar activity (1991), the values of Lyapunov exponent for AE index time series representing quiet conditions (yearly mean = 0.5±0.1 min −1 ) have no significant difference from those values for corresponding storm conditions (yearly mean = 0.5±0.17 min −1 ). This implies that, for the cases considered here, geomagnetic storms may not be an additional source to increase or decrease the deterministic chaotic aspects of magnetosphere, especially during high solar activity. During solar minimum period (1994), the seasonal mean value of Lyapunov exponent for AE index time series belong to quiet periods in winter (0.7±0.11 min −1 ) is higher compared to corresponding value of storm periods in winter (0.36±0.09 min −1 ). This may be due to the fact that, stochastic part, which is D st dependent could be more prominent during storms, thereby increasing fluctuations/stochasticity and reducing determinism in AE index time series during storms. It is observed that, during low solar active period (1994), the seasonal mean value of entropy for time series representing storm periods of equinox is greater than that for quiet periods. However, significant difference is not observed between storm and quiet time values of entropy during high solar activity (1991), which is also true for nonlinear prediction error for both low and high solar activities. In the case of both high and low solar activities, the higher standard deviations of yearly mean Lyapunov exponent values for AE index time series for storm periods compared to those for quiet periods might be due to the strong interplay between stochasticity and determinism during storms.Correspondence to: K. Unnikrishnan (kaleekkal unni@yahoo.com) It is inferred that, the external driving forces, mainly due to solar wind, make the solar-magnetosphere-ionosphere coupling more complex, which generates many active degrees of freedom with various levels of coupling among them, under various physical conditions. Hence, the superposition of a large number of active degrees of freedom can modify the stability/instability conditions of magnetosphere.

The comparative study of chaoticity and dynamical complexity of the low-latitude ionosphere, over Nigeria, during quiet and disturbed days

“…The ionosphere is a system that can also be described by similar dynamical processes as the magnetosphere, as both systems are also coupled (Unnikrishnan, 2010). Some of the investigations carried out on the chaoticity of both the ionosphere and the magnetosphere have yielded similar results for storm and quiet periods (Unnikrishnan, 2008(Unnikrishnan, , 2010. It implies that one can use similar methods to study the ionosphere and magnetosphere, and this informs the use of Tsallis entropy to study the ionosphere in this work, since it has been used to describe the magnetosphere.…”

“…This is also evident in the study on magnetospheric dynamics and the ionosphere in the past decade. The study of chaos in magnetospheric index time series such as the AE index and the AL index was initially conducted by Vassiliadis et al (1990), Shan et al (1991), Pavlos et al (1992) and Unnikrishnan (2008). These efforts have led to further advances in the study of chaos in the upper atmosphere.…”

Chaotic behaviour of interplanetary magnetic field under various geomagnetic conditions

“…time delayed mutual information and the false nearest neighbour method), it is observed that any delay tZ25 and any dimension mZ3 are the suitable choices for t and m, respectively, for both IMF 9B9 and B z time series. By repeating the similar analysis for all the time series considered in the present study, these choices for t and m are found to be true (Unnikrishnan et al, 2006a(Unnikrishnan et al, , 2006bUnnikrishnan, 2008). Hence, the choice of t as 40 and m as 4 for further analysis of this study are reasonable.…”

“…Unnikrishnan (2008) observed that during high solar activity (1991), the values of Lyapunov exponent for AE index time series, representing the magnetopseric dynamics for quiet conditions have no significant difference from the corresponding storm conditions. This implies that geomagnetic storms may not be an additional source to increase or decrease the deterministic chaotic aspects of magnetosphere during high solar activity.…”

“…Unnikrishnan (2008) analyzed the deterministic chaotic behaviour of magnetosphere using AE index time series. The significant chaotic quantifiers like Lyapunov exponent, spatiotemporal entropy and non-linear prediction error for AE index time series under various physical conditions were also estimated and compared.…”