1 citations · 2 across the 17 of their papers we have counts for
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A New Route to Chaos through the Geometric Composition of Non-Normal Amplification
D. Sornette, V. R. Saiprasad, V. Troude
Chaos emerges when stretching is repeatedly recycled by reinjection. We uncover a new route to chaos in which the decisive variable is the temporal order of non-normal tangent maps…
Non-Normal Route to Chaos
D. Sornette, V. R. Saiprasad, V. Troude
Deterministic chaos is usually associated with local spectral expansion: Jacobian eigenvalues are expected to exceed unity somewhere on the attractor. We show that this view is inc…
Eigenvector Geometry as a New Route to Criticality in Random Multiplicative Systems
Virgile Troude, Didier Sornette
Heavy-tailed fluctuations and power law distributions pervade physics, biology, and the social sciences, with numerous mechanisms proposed for their emergence. Kesten processes, wh…
Unifying Framework for Amplification Mechanisms: Criticality, Resonance and Non-Normality
Virgile Troude, Didier Sornette
We bring together three key amplification mechanisms in linear dynamical systems: spectral criticality, resonance, and non-normality. We present a unified linear framework that bot…
Illusions of Criticality: Crises Without Tipping Points
Virgile Troude, Sandro Claudio Lera, Ke Wu +1
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…