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Critical slowing down indicators in synchronous period-doubling for salamander flicker vision

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Abstract

Many dynamical systems, particularly biological ones, exhibit different regimes in which the dynamics of the system vary from one regime to another through a critical transition. These transitions are critical points (CPs). The CPs can be observed with a critical slowing down phenomenon in which the attractor gets fragile. Due to the importance of CPs, different indicators such as variance, autocorrelation, kurtosis, and skewness have been studied over the years. In this paper, four reputed CP indicators are investigated on electroretinograms (ERGs), recorded from the salamander’s eyes. To investigate the capability of these famous indicators for anticipating the changes in the system’s dynamics of salamander’s ERGs bifurcation, first, different dynamics of the system are detected using manual thresholding. Then the early warning signals are implemented using the four indicators. The results indicate the promising ability of the variance indicator as a trustworthy index that can be considered as an early warning signal. Moreover, it turns out that the kurtosis and skewness are the least promising indicators since they are so sensitive to noise, which is an intrinsic property of the real data. Although autocorrelation leads to accurate results as variance does, it includes many false-positives, which reduce this indicator’s reliability to be considered as an early warning signal of CPs. Furthermore, it is specified that the proper length of data in each bifurcation parameter will lead to a more credible early warning signal.

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Acknowledgements

This work is partially funded by the Center for Nonlinear Systems, Chennai Institute of Technology, India vide funding number CIT/CNS/2021/RD/007.

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Authors and Affiliations

  1. Biomedical Engineering Department, Amirkabir University of Technology, Tehran, Iran

    Mahtab Mehrabbeik, Fahimeh Nazarimehr & Sajad Jafari

  2. Center for Artificial intelligence, Chennai Institute of Technology, Chennai, India

    Ramesh Ramamoorthy

  3. Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, India

    Karthikeyan Rajagopal

  4. Health Technology Research Institute, Amirkabir University of Technology, Tehran, Iran

    Sajad Jafari

  5. Department of Mathematics, Statistics and Physics, Qatar University, Doha, 2713, Qatar

    Iqtadar Hussain

Authors
  1. Mahtab Mehrabbeik
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  2. Ramesh Ramamoorthy
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  3. Karthikeyan Rajagopal
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  4. Fahimeh Nazarimehr
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  5. Sajad Jafari
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  6. Iqtadar Hussain
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Contributions

MM and FN developed the theory. RR and KR performed the computations. IH verified the analytical methods. IH and KR conceived of the presented idea. SJ supervised the work. All authors discussed the results of the paper. MM and FN wrote the original draft with input from all authors, and all the authors reviewed and edited it.

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Correspondence to Sajad Jafari.

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Mehrabbeik, M., Ramamoorthy, R., Rajagopal, K. et al. Critical slowing down indicators in synchronous period-doubling for salamander flicker vision. Eur. Phys. J. Spec. Top. 230, 3291–3298 (2021). https://doi.org/10.1140/epjs/s11734-021-00113-0

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  • DOI: https://doi.org/10.1140/epjs/s11734-021-00113-0

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