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Frequency and wavelet based analyses of partial and complete measure synchronization in a system of three nonlinearly coupled oscillators

De, Sadhitro and Gupta, Shraddha and Janaki, MS and Iyengar, Sekar AN (2018) Frequency and wavelet based analyses of partial and complete measure synchronization in a system of three nonlinearly coupled oscillators. In: CHAOS, 28 (11).

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Official URL: http://dx.doi.org/10.1063/1.5049800

Abstract

Measure Synchronization (MS) is the generalization of synchrony to Hamiltonian Systems. Partial measure synchronization (PMS) and complete measure synchronization in a system of three nonlinearly coupled one-dimensional oscillators have been investigated for different initial conditions on the basis of numerical computation. The system is governed by the classical SU(2) Yang-Mills-Higgs (YMH) Hamiltonian with three degrees of freedom. Various transitions in the quasiperiodic (QP) region, namely, QP unsynchronized to PMS, PMS to PMS, and PMS to chaos are identified through the average bare energies and interaction energies route maps as the coupling strength is varied. The transition from quasiperiodicity to chaos is seen to be associated with a gradual transition to complete chaotic measure synchronization (CMS) which is followed by chaotic unsynchronized states, the most stable state in this case. The analyses illustrate the dependence on initial conditions. The explanation of the behavior in the QP regime is sought from the power spectral analysis. The existence of PMS is confirmed using the order parameter M (here M-alpha beta for different combination pairs of oscillators), best suited to identify MS in coupled two-oscillator systems, and this definition is extended to obtain a new order parameter, M-3, aiding to distinguish complete MS of three oscillators from other forms of motion. The study of wavelet coefficient spectra sheds new light on the relative phase information of the oscillators in the QP PMS regions, also highlighting the intertwined role played by the various frequency components and their amplitudes as they vary temporally. Furthermore, this technique helps to draw a sharp distinction between CMS and chaotic unsynchronized states. Based on the Continuous Wavelet Transform coefficients of the three oscillators, an order parameter M-wav is defined to indicate the extent of synchronization of the various scales (frequencies) for different coupling strengths in the chaotic regime. Published by AIP Publishing.

Item Type: Journal Article
Additional Information: The copyright for this article belongs to AMER INST PHYSICS
Keywords: HAMILTONIAN SYSTEMS
Department/Centre: Division of Physical & Mathematical Sciences > Physics
Depositing User: Id for Latest eprints
Date Deposited: 24 Dec 2018 16:19
Last Modified: 24 Dec 2018 16:19
URI: http://eprints.iisc.ac.in/id/eprint/61308

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