Pseudo-Bifurcations in Stochastic Non-Normal Systems

Abstract: We challenge the prevailing emphasis on bifurcations as the primary mechanism behind many abrupt changes in complex systems and propose an alternative, more universally applicable explanation based on non-normal dynamics. We demonstrate that linear or approximately linear stochastic systems near a dynamical attractor exhibit transient repulsive dynamics - termed pseudo-bifurcations - when interacting components are sufficiently asymmetric and hierarchically organized, i.e., non-normal. These pseudo-bifurcations produce early-warning signals commonly linked to bifurcations, such as dimension reduction, critical slowing down, and increased variance. Furthermore, we show that, as actual bifurcations approach, non-normal transients also emerge, complicating their distinction and potentially creating a bias that suggests the system is much closer to a critical point than it actually is. We support our analytical derivations by empirically demonstrating that the brain exhibits clear signs of such non-normal transients during epileptic seizures. Many systems suspected of approaching critical bifurcation points should be reconsidered, as non-normal dynamics offer a more generic explanation for the observed phenomena across natural, physical, and social systems.