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Can Lyapunov exponent predict critical transitions in biological systems?

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Abstract

Transitions from one dynamical regime to another one are observed in many complex systems, especially biological ones. It is possible that even a slight perturbation can cause such a transition. It is clear that this can happen to an object when it is close to a tipping point. There is a lot of interest in finding ways to recognize that a tipping point (in which a bifurcation occurs) is near. There is a possibility that in complex systems, a phenomenon known as “critical slowing down” may be used to detect the vicinity of a tipping point. In this paper, we propose Lyapunov exponents as an indicator of “critical slowing down.”

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Acknowledgements

The authors would like to thank Dr. Leslie Samuel Smith for the help and edits.

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Authors and Affiliations

  1. Biomedical Engineering Department, Amirkabir University of Technology, Tehran, 15875-4413, Iran

    Fahimeh Nazarimehr, Sajad Jafari & Seyed Mohammad Reza Hashemi Golpayegani

  2. Department of Physics, University of Wisconsin - Madison, Madison, WI, 53706, USA

    J. C. Sprott

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  1. Fahimeh Nazarimehr
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  2. Sajad Jafari
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  3. Seyed Mohammad Reza Hashemi Golpayegani
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  4. J. C. Sprott
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Correspondence to Sajad Jafari.

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Nazarimehr, F., Jafari, S., Hashemi Golpayegani, S.M.R. et al. Can Lyapunov exponent predict critical transitions in biological systems?. Nonlinear Dyn 88, 1493–1500 (2017). https://doi.org/10.1007/s11071-016-3325-9

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