The transition from homeostasis to stochasticity induced catastrophe

Abstract

What are the signatures of the onset of catastrophe? Here we present the rich system physics characterizing the transition from homeostasis to stochasticity driven breakdown in an experimentally motivated minimal model. Recent high-precision experiments on individual bacterial cells, growing and dividing repeatedly in a variety of environments, have revealed a previously unknown intergenerational scaling law which not only uniquely determines the stochastic map governing homeostasis, but also, as we show here, offers quantitative insights into the transition from the "conspiracy principle" regime (homeostasis) to the "catastrophe principle" regime and then to system breakdown. In fact, upon closer examination, the stochastic map turns out to be a one-dimensional Kesten process; these transitions occur as a single parameter, the strength of the multiplicative noise term, is continuously tuned. Emergence of asymptotically scale invariant distributions with quantifiable power law tails, outlier driven extremal behavior and reverse monotonicity of the conditional exceedance distribution characterize this transition to catastrophe. In turn, prevention of rapid increase in the extremal event-driven rate of failure, in the interest of system preservation, causes the catastrophe regime to be strategically unfavorable.