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
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.”