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Effect of amplitude and frequency of limit cycle oscillators on their coupled and forced dynamics

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Abstract

The occurrence of synchronization and amplitude death phenomena due to the coupled interaction of limit cycle oscillators (LCO) has received increased attention over the last few decades in various fields of science and engineering. Studies pertaining to these coupled oscillators are often performed by studying the effect of various coupling parameters on their mutual interaction. However, the effect of system parameters (i.e., the amplitude and frequency) on the coupled interaction of such LCO has not yet received much attention, despite their practical importance. In this paper, we investigate the dynamical behavior of time-delay coupled Stuart–Landau (SL) oscillators exhibiting subcritical Hopf bifurcation for the variation of amplitude and frequency of these oscillators in their uncoupled state. For identical SL oscillators, a gradual increase in the amplitude of LCO shrinks the amplitude death regions observed between the regions of in-phase and anti-phase synchronization leading to its eventual disappearance, resulting in the occurrence of phase-flip bifurcations at higher amplitudes of LCO. We also observe an alternate existence of in-phase and anti-phase synchronization regions for higher values of time delay, whose prevalence of occurrence increases with an increase in the frequency of the oscillator. With the introduction of frequency mismatch, the region of amplitude death. The forced response of SL oscillator shows an asymmetry in the Arnold tongue and the manifestation of asynchronous quenching of LCO. An increase in the amplitude of LCO narrows the Arnold tongue and reduces the region of asynchronous quenching observed in the system. Finally, we compare the coupled and forced response of SL oscillators with the corresponding experimental results obtained from laminar thermoacoustic oscillators and the numerical results from van der Pol (VDP) oscillators. We show that the SL model qualitatively displays many features observed experimentally in coupled and forced thermoacoustic oscillators. In contrast, the VDP model does not capture most of the experimental results due to the limitation in the independent variation of system parameters.

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Acknowledgements

We gratefully acknowledge the Office of Naval Research Global (ONRG) USA (N62909-18-1-2061, Contract Monitor: Dr. R. Kolar) and J. C. Bose fellowship (JCB /2018/000034/SSC) from Department of Science and Technology (DST) India for the financial support.

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  1. Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, 600 036, India

    D. Premraj, Krishna Manoj, Samadhan A. Pawar & R. I. Sujith

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  1. D. Premraj
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  2. Krishna Manoj
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Correspondence to Samadhan A. Pawar.

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Premraj, D., Manoj, K., Pawar, S.A. et al. Effect of amplitude and frequency of limit cycle oscillators on their coupled and forced dynamics. Nonlinear Dyn 103, 1439–1452 (2021). https://doi.org/10.1007/s11071-020-06135-y

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