Can Lyapunov exponent predict critical transitions in biological systems?

Fahimeh Nazarimehr, Sajad Jafari, Sayed Mohammad Reza Hashemi Golpayegani
Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran

J. C. Sprott
Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA

Received: 15 July 2016 / Accepted: 27 December 2016 / Published online: 7 January 2017


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.”

Ref: F. Nazarimehr, S. Jafari, S. M. R. H. Golpayegani, and J. C. Sprott, Nonlinear Dynamics 88, 1493-1500 (2017)

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