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Limit cycles and chaos induced by a nonlinearity with memory

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Abstract

Inspired by the recent observation of memory effects in the nonlinear optical response of a coherently-driven micro-cavity, we investigate the effects of varying the memory time on the dynamics of optical and mechanical resonators. For a memory time that is commensurate with the inverse dissipation rate, both optical and mechanical resonators display stable limit cycles. In this regime, we evidence a cascade of period-doubling bifurcations as the memory time increases. For longer memory times, the mechanical resonator displays a regime of chaotic dynamics associated with a double scroll attractor. We also analyze the effects of the memory time on the spectrum and oscillation amplitude of the oscillator. Our results point to new opportunities for nonlinear energy harvesting, provided that a nonlinearity with memory can be implemented in mechanical systems.

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Acknowledgements

This work is part of the research programme of the Netherlands Organisation for Scientific Research (NWO). We thank Carlos Pando Lambruschini and Panayotis Panayotaros for organizing the workshop on Advanced Computational and Experimental Techniques in Nonlinear Dynamics, which stimulated this manuscript. We also thank Jason Smith, Aurelien Trichet, and Kiana Malmir for providing the concave mirror used for the experiments in Fig. 1. SRKR acknowledges an ERC Starting Grant with project number 85269.

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  1. Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG, Amsterdam, The Netherlands

    K. J. H. Peters & S. R. K. Rodriguez

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Peters, K.J.H., Rodriguez, S.R.K. Limit cycles and chaos induced by a nonlinearity with memory. Eur. Phys. J. Spec. Top. 231, 247–254 (2022). https://doi.org/10.1140/epjs/s11734-021-00407-3

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