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Invariant Tori in a Network of Two Spin-Torque Nano Oscillators

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Proceedings of the 4th International Conference on Applications in Nonlinear Dynamics (ICAND 2016) (ICAND 2016)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 6))

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Abstract

Over the past few years it has been shown, through theory and experiments, that the AC current produced by spin torque nano-oscillators (STNO), coupled in an array, can lead to feedback between the STNOs causing them to synchronize and that, collectively, the microwave power output of the array is significantly larger than that of an individual oscillator. Other works have pointed, however, to the difficulty in achieving synchronization. In particular, Persson et al. [17] shows that the region of parameter space where the synchronization state exists for even a small array with two STNOs is rather small. In this work we explore in more detail the nature of the bifurcations that lead into and out of the synchronization state for the two-array case. The bifurcation analysis shows bistability between in-phase and out-of-phase oscillations. A more detailed analysis of the out-of-phase solutions reveals both limit-cycles and invariant tori that are responsible for anti-phase and quasi-periodic oscillations respectively. A continuation of unstable tori demonstrates a portion of the separatrix bounding the basins of attraction for the in- and out-of-phase limit-cycles.

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Author information

Authors and Affiliations

  1. Predictive Science Inc., 9990 Mesa Rim Rd, San Diego, CA, 92121, USA

    James Turtle

  2. San Diego State University, San Diego, CA, 92182, USA

    Antonio Palacios

  3. Space and Naval Warfare Systems Center Pacific, Code 71730, 53560 Hull Street, San Diego, CA, 92152-5001, USA

    Patrick Longhini & Visarath In

Authors
  1. James Turtle
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  2. Antonio Palacios
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  3. Patrick Longhini
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  4. Visarath In
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Corresponding author

Correspondence to James Turtle .

Editor information

Editors and Affiliations

  1. Code 2363, Space and Naval Warfare Systems Center Code 2363, San Diego, California, USA

    Visarath In

  2. Code 2363, Space and Naval Warfare Systems Center , San Diego, California, USA

    Patrick Longhini

  3. Department of Mathematics & Statistics, San Diego State University , San Diego, California, USA

    Antonio Palacios

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Turtle, J., Palacios, A., Longhini, P., In, V. (2017). Invariant Tori in a Network of Two Spin-Torque Nano Oscillators. In: In, V., Longhini, P., Palacios, A. (eds) Proceedings of the 4th International Conference on Applications in Nonlinear Dynamics (ICAND 2016). ICAND 2016. Lecture Notes in Networks and Systems, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-52621-8_1

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  • DOI: https://doi.org/10.1007/978-3-319-52621-8_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-52620-1

  • Online ISBN: 978-3-319-52621-8

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