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Unraveling the Chaos-Land and Its Organization in the Rabinovich System

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Advances in Dynamics, Patterns, Cognition

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 20))

Abstract

A suite of analytical and computational techniques based on symbolic representations of simple and complex dynamics is further developed and employed to unravel the global organization of bi-parametric structures that underlie the emergence of chaos in a simplified resonantly coupled wave triplet system, known as the Rabinovich system. Bi-parametric scans reveal the stunning intricacy and intramural connections between homoclinic and heteroclinic connections, and codimension-2 Bykov T-points and saddle structures, which are the prime organizing centers of complexity of the bifurcation unfolding of the given system. This suite includes Deterministic Chaos Prospector (DCP) to sweep and effectively identify regions of simple (Morse-Smale) and chaotic structurally unstable dynamics in the system. Our analysis provides striking new insights into the complex behaviors exhibited by this system, that are hitherto unexplored.

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Acknowledgements

AS acknowledges the financial support from RSF grant 14-41-00044 at the Lobachevsky University of Nizhny Novgorod, as well as NSF BIO-DMS grant IOS-1455527. We thank the acting members of the NEURDS (Neuro Dynamical Systems) lab at GSU for helpful discussions and proof-reading the manuscript. We are very thankful to Sunitha Basodi for her deep insights into the computational aspects of GPU programming, and the Periodicity Correction algorithm. We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Tesla K40 GPU used in this research.

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Authors and Affiliations

  1. Neuroscience Institute, Georgia State University, Petit Science Center, 100 Piedmont Av., Atlanta, GA, 30303, USA

    Krishna Pusuluri

  2. Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str 24/25, Bld. 28, Potsdam, 14476, Germany

    Arkady Pikovsky

  3. Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Petit Science Center, 100 Piedmont Av., Atlanta, GA, 30303, USA

    Andrey Shilnikov

Authors
  1. Krishna Pusuluri
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  2. Arkady Pikovsky
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  3. Andrey Shilnikov
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Corresponding author

Correspondence to Krishna Pusuluri .

Editor information

Editors and Affiliations

  1. Pennsylvania State University, University Park, Pennsylvania, USA

    Igor S. Aranson

  2. Institute for Physics and Astronomy, University of Potsdam, Potsdam, Germany

    Arkady Pikovsky

  3. BioCircuits Institute, University of California San Diego, La Jolla, California, USA

    Nikolai F. Rulkov

  4. BioCircuits Institute, University of California San Diego, La Jolla, California, USA

    Lev S. Tsimring

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Pusuluri, K., Pikovsky, A., Shilnikov, A. (2017). Unraveling the Chaos-Land and Its Organization in the Rabinovich System. In: Aranson, I., Pikovsky, A., Rulkov, N., Tsimring, L. (eds) Advances in Dynamics, Patterns, Cognition. Nonlinear Systems and Complexity, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-53673-6_4

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  • DOI: https://doi.org/10.1007/978-3-319-53673-6_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53672-9

  • Online ISBN: 978-3-319-53673-6

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