📝 SummarXiv

Abstract

Abrupt shifts in ecosystems, brains, markets, and climate are often diagnosed as signs of approaching a tipping point, i.e. a critical bifurcation where stability is lost. Here we reveal a broader and more deceptive mechanism: pseudo-bifurcations. In stochastic non-normal systems, asymmetric interactions produce transient episodes of apparent instability despite long-term stability. We show analytically, numerically, and with empirical evidence from brain dynamics during epileptic seizures that pseudo-bifurcations reproduce the full set of early-warning signals usually taken as proof of proximity to tipping points, including critical slowing down, increased variance, and dimensional collapse. Crucially, these false alarms can occur well before any true bifurcation, systematically biasing crisis diagnosis. This discovery reframes how abrupt transitions are interpreted across disciplines: what has long been attributed to ``criticality'' may instead reflect the hidden geometry of non-normal dynamics. By uncovering this illusion of criticality, we call for a fundamental reassessment of how crises are identified, predicted, and managed in natural, social, and technological systems.