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Measure synchronization in interacting Hamiltonian systems: A brief review

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  • Ghosh, Anupam

Abstract

This paper aims to review the measure synchronization, a weak form of synchronization observed in coupled Hamiltonian systems, briefly. This synchronization is characterized by a Hamiltonian system that displays either quasiperiodic or chaotic dynamics. Each system, in the presence of either linear or nonlinear coupling, shares a phase space domain with an identical invariant measure in the measure synchronized state. It is important to note that while the trajectories are identical in measure, they do not necessarily exhibit complete temporal synchrony. This synchronization has been observed in various physical systems, such as coupled pendulums, Josephson junctions, and lasers.

Suggested Citation

  • Ghosh, Anupam, 2023. "Measure synchronization in interacting Hamiltonian systems: A brief review," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011396
    DOI: 10.1016/j.chaos.2023.114237
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    References listed on IDEAS

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    1. Anupam Ghosh & Sagar Chakraborty, 2020. "Comprehending deterministic and stochastic occasional uncoupling induced synchronizations through each other," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(6), pages 1-14, June.
    2. González-Avella, J.C. & Cosenza, M.G. & San Miguel, M., 2014. "Localized coherence in two interacting populations of social agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 399(C), pages 24-30.
    3. Parastesh, Fatemeh & Azarnoush, Hamed & Jafari, Sajad & Hatef, Boshra & Perc, Matjaž & Repnik, Robert, 2019. "Synchronizability of two neurons with switching in the coupling," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 217-223.
    4. Ghosh, Anupam & Sujith, R.I., 2020. "Emergence of order from chaos: A phenomenological model of coupled oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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