Early signatures of regime shifts in complex dynamical systems

Abstract

A large number of studies have recently been carried out on the early signatures of regime shifts in a number of dynamical systems, e.g., ecosystems, the climate, fish and wildlife populations, financial markets, complex diseases and gene circuits. The underlying model in most cases is that of the fold-bifurcation in which a sudden regime shift occurs at a bifurcation point. The shift involves a discontinuous jump from one type of stable steady state to another. The dynamics of natural systems have both deterministic and stochastic components. The early signatures of abrupt regime shifts include the critical slowing down as a transition point is approached, rising variance and the lag-1 autocorrelation function, increased skewness of the steady-state probability distribution and the ratio of two mean first passage times for the exits from the stable steady states as the bifurcation point is approached. Noise-induced regime shifts are also possible for which the vicinity of the bifurcation point is not essential. In this paper, we review examples of regime shifts in natural systems and the associated early signatures. We further discuss how such approaches provide useful insights on a cell biological process involving the fold-bifurcation.