Synchronization Effects in the Interaction of Complex Nonlinear Systems

Abstract

This study investigates the fundamental mechanisms of synchronization in nonlinear dynamical systems under external influences, bridging theoretical analysis with real-world geophysical applications. We first focus on the van der Pol nonlinear oscillator to explore forced synchronization, employing numerical modeling to analyze how external periodic forces modify the system's phase and frequency dynamics. A key finding reveals that the introduction of random noise can, counter-intuitively, contribute to the regulation of complex or chaotic regimes, leading to enhanced stability. Extending this analysis to the Sun-Earth connection, we utilize the wavelet coherence method to quantitatively assess the time-frequency coherence between solar parameters (such as the f10.7 index and the IMF  component) and terrestrial responses. This analysis successfully detects significant synchronization effects, confirming that the coherent interaction between these systems is directly responsible for triggering geomagnetic storms. Overall, this work provides a comprehensive framework for understanding synchronization phenomena, from controlled nonlinear systems to large-scale astrophysical interactions.