Emergent Synchronization in Inductively Coupled Heterogeneous Oscillators

Inductively coupled heterogeneous oscillators hold promise for applications in distributed sensing, neuro-computing, and neural networks. This study explores synchronization between two fundamentally different systems: a chaotic Chua oscillator and a periodic LC circuit, coupled through an inductor. A generalized framework is developed to describe such interactions, and conditions for the existence of a synchronization manifold are derived. Linear stability analysis reveals that transverse deviations from the manifold oscillate with a frequency proportional to the square root of the coupling strength. This prediction is verified numerically using Hilbert transform analysis to estimate the mean frequency of transverse deviations across a range of coupling strengths. Further, frequency spectrum analysis reveals multiple common frequencies between the two systems, indicating phase synchronization. Notably, the natural frequency of the LC circuit does not appear in the Chua oscillator's spectrum, suggesting unidirectional influence. Due to the lack of a well-defined rotation center in the double-scroll attractor, empirical mode decomposition (EMD) is employed to extract phase information. This analysis uncovers a novel mode-based phase synchronization, where the lowest mode remains desynchronized while the second-lowest mode exhibits strong phase locking within specific coupling ranges. The phase locking value (PLV) supports this observation, highlighting high synchrony over a broad range. While the manifold assumption enables a tractable analysis, the full dynamics are more nuanced, indicating correlated yet non-identical evolution. These results offer new insights into synchronization behavior in hybrid dynamical systems and suggest potential applications in complex heterogeneous networks.