The MLE and ApEn values of the D_st indicate that chaotic and dynamical complexity responses are high during minor geomagnetic storms, reduce at moderate geomagnetic storms and decline further during major geomagnetic storms. However, the MLE and ApEn values obtained from solar wind electric field (VB_s) indicate that chaotic and dynamical complexity responses are high with no significant difference between the periods that are associated with minor, moderate and major geomagnetic storms.