Nonlinear and Causal Dynamics between Solar and Geomagnetic Activity Indices: Findings from Chaos and Causality Measures

This study aims to identify nonlinear/chaotic features and causal relationships among monthly SSN, F10.7, aa, and Dst indices over December 1963-March 2025.Phase-space is reconstructed via AMI-selected delay and FNN dimension ; we estimate the Hurst exponent , the largest Lyapunov exponent , and the correlation dimension 2 ; and apply CCM with SSN as reference. spans 0.84-0.93( 0.93; 10.7 0.93; 0.88; 0.84), indicating strong persistence. ranges from 0.010 to 0.040 (highest for Dst, lowest for aa), implying deterministic chaos with finite prediction horizons. 2 varies between 3.37-3.86,consistent with low-moderate dimensional structure.CCM analysis shows a strong linear relationship between SSN-F10.7, while indicating a non-linear causal relationship between SSN and other indices.In conclusion, sunspot variability affects global geomagnetic activity continuously and nonlinearly on a monthly scale; this effect is most pronounced for aa and weaker for Dst.