Relaxation time as an indicator of critical transition to a eutrophic
lake state: The role of stochastic resonance

Zhiqin Ma1, Chunhua Zeng1 (a) and Bo Zheng2,3 (b)

1 Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
2 School of Physics and Astronomy, Yunnan University, Kunming 650091, Peoples Republic of China
3 Department of Physics, Zhejiang University, Hangzhou 310027, Peoples Republic of China

Abstract – Lake ecosystems exhibit the nonlinear responses and may undergo catastrophic shifts
to opposite states from which recovery is difficult. Recent theoretical and experimental developments have revealed that characterizing the resilience of ecosystems can provide a way to anticipate
critical transitions. In this letter, we present a novel and practical approach that measures the
resilience, i.e., the relaxation time as an indicator of a critical transition to a eutrophic lake state.
Furthermore, the possible mechanisms underlying these findings are explored via stochastic resonance, namely, signal-to-noise ratio as a function of the system parameter shows a maximum value when the noise intensity is fixed. The results show that relaxation time is an excellent indicator,
and stochastic resonance occurs near a critical threshold. Our results offer a new perspective to
anticipate critical transitions in ecosystems.