Pseudo-bifurcations in stochastic non-normal systems and the limits of early-warning signals

Early-warning indicators in ecosystems, neural activity, financial markets, and climate systems are often interpreted as evidence that a system is approaching a tipping point, typically understood as a bifurcation at which a previously stable state loses stability or disappears. Such indicators include increased variance, autocorrelation, and dimensional reduction. Here we identify a different mechanism that generates the same statistical signatures without any loss of stability. In stochastic non-normal dynamical systems, asymmetric interactions produce transient amplification that creates episodes of apparent instability despite the persistence of a stable attractor. We refer to these episodes as pseudo-bifurcations. Through analytical results, numerical simulations, and empirical evidence from brain dynamics during epileptic seizures, we show that pseudo-bifurcations reproduce the canonical early-warning signals commonly associated with bifurcation-induced tipping points. Crucially, these signatures arise while the underlying system remains dynamically stable and far from any bifurcation. These results demonstrate that widely used early-warning indicators are not uniquely diagnostic of tipping points. Instead, they may reflect the transient geometry of non-normal dynamics, which are ubiquitous in complex interacting systems. Early-warning indicators such as increased variance, autocorrelation, and dimensional reduction are often interpreted as signs that complex systems in ecology, neuroscience, finance, or climate are approaching a tipping point at which a stable state loses stability or disappears. Here, the authors demonstrate, using brain dynamics during epileptic seizures as an example case, that the same statistical signatures can arise from pseudo-bifurcations in stochastic non-normal systems, showing that these widely used indicators are not uniquely diagnostic of tipping points.