Sensitivity Analysis of Coupled Nonlinear Oscillators

This study investigates the synchronization behavior of coupled nonlinear oscillators, focusing on the sensitivity of synchronization to system parameters and coupling strength. Employing Floquet theory and numerical simulations, we analyze both homogeneous and heterogeneous oscillator systems. Our results demonstrate that synchronization depends on specific parameter ranges and coupling gain values. We establish bounds for these parameters, offering insights into reliable synchronization conditions. This work advances our understanding of coupled nonlinear systems with potential applications in neuroscience and electrical engineering fields. While limited to specific oscillator models and parameter spaces, our findings motivate future research. Expanding the scope to diverse models and broader parameter ranges, alongside pursuing analytical solutions, promises to generalize the observed behaviors and provide deeper mathematical insights into synchronization mechanisms.