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Feb 17, 2026Keywords:
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Measure Synchronization in a Coupled Helmholtz Resonator Hamiltonian
Abstract
Background: Measure synchronization (MS) is a weak form of synchronization that is observed in coupled Hamiltonian systems, where the trajectories share the same phase space without perfectly locking.
Objective: In this study, MS was investigated in a pair of nonlinearly coupled Helmholtz resonators described by a quartic Hamiltonian.
Methods: By varying the coupling strength k, the distinct dynamical regimes such as quasiperiodic unsynchronized states, quasiperiodic measure synchronized (QPMS), chaotic unsynchronized states, and chaotic measure synchronized states (CMS) were identified. We characterized these transitions between these states using, average bare energy, Lyapunov exponent, phase portraits, power spectra, and wavelet transforms.
Results: The results reveal that MS emerges when the coupling strength exceeds a critical threshold, leading to energy redistribution and alignment in the system dynamics despite their chaotic or quasiperiodic nature.
Conclusion: This work contributes to a broader understanding of synchronization in Hamiltonian systems and highlights the role of nonlinear coupling in the dynamics of collective behavior.
