arXiv subjects

D. Sornette

Publications and source records attributed to D. Sornette.

At least 19 recordsLinked to original sources

arXiv2026

A New Route to Chaos through the Geometric Composition of Non-Normal Amplification

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: periodic and chaotic states can share essentially the same one-step stretching statistics while their ordered products acquire opposite Lyapunov growth. We introduce the ordered-product growth rate $h_L$ over $L$ successive tangent maps, which reveals how states indistinguishable at one step separate under geometric composition and identifies the finite composition scale at which chaos emerges. We use this mechanism to establish a new form of global chaos control: minute phase actions reorient the successive non-normal amplification directions so that their geometric composition becomes contracting, suppressing chaos at fixed dissipation without reducing local amplification or targeting a preselected orbit.

nlin.CD↗

arXiv2026

No persistent circadian oscillator at genome resolution: pseudo-coherence in gut microbiome dynamics

Diurnal rhythms in the gut microbiome are commonly read as evidence of host-driven entrainment or of microbial oscillators that synchronise to a common clock. We reanalyse hourly genome-resolved (MAG-level) mouse-gut time series with diagnostics tailored to test that interpretation. At this resolution and for both animals in the dataset, the time-frequency representation carries no persistent ridge; the time-averaged spectrum is enhanced at low frequencies and depleted at intermediate frequencies; the lagged covariance is markedly time-asymmetric, with a global imbalance peak near tens of hours; and an amplitude-adjusted Fourier surrogate test identifies a weak time-averaged construction in the candidate circadian band, never as a fixed time-frequency ridge. The two functional guilds that carry the inferred non-normal amplification are identified independently by the rankings of two inferred dynamical modes (the reaction mode, into which fluctuations are transiently amplified, and the non-normal mode, which injects them), and recover the primary polysaccharide degraders of Bacteroidota and the secondary butyrate and propionate fermenters of Bacillota A without invoking any phase information. The conjunction of these signatures matches a stable but strongly non-normal stochastic regime, that is, pseudo-coherence: geometric amplification reshapes stochastic fluctuations onto a low-dimensional reaction subspace, producing intermittent synchronisation-like episodes, broken time-reversal symmetry, and emergent time-averaged characteristic scales without an underlying oscillator. We propose a falsifiable test via high-resolution clock-gene-knockout cohorts.

physics.bio-ph↗

arXiv2026

Inferring Non-Normal Amplification Geometry from Multivariate Time Series

Across hydrodynamics, ecology, neuroscience, network dynamics, non-Hermitian physics, and socio-economic systems, asymptotically stable dynamics can exhibit large transient amplifications that are invisible to eigenvalue-based analyses. The mechanism is geometric rather than spectral: perturbations entering along one direction may be expressed transiently along another, allowing asymptotic decay to coexist with strong transient or noise-driven amplification. We introduce non-normal directional response inference, a data-driven method for detecting this geometry from multivariate time series when the governing operator is unknown. A local linear operator is estimated from sliding windows and projected onto the dominant two-dimensional input-response subspace. The reduced dynamics are summarized by the eigenvalue splitting $Δ$, eigenvector non-orthogonality $K$, and the scale-free ratio $R=K/K_c(Δ)$, where $K_c(Δ)$ is the two-dimensional threshold for transient amplification. Controlled benchmarks show that the reduced geometry, particularly $R$, can be recovered from finite data even when the full high-dimensional operator is poorly estimated. Tests across sample size, dimension, training horizon, spectral structure, and non-stationarity confirm that the relevant response geometry requires far fewer observations than full-matrix recovery. Applied in moving windows to electrohysterogram, seizure EEG, freezing-of-gait, and unstable push-up inertial recordings, the method reveals systematic changes around known physiological or behavioral episodes through shifts in $R$, changes in $Δ$, or stronger projection of fluctuations onto the inferred response direction. It thus exposes interpretable changes in local response geometry without framing the problem as supervised event detection.

physics.data-an↗

arXiv2026

Non-Normal Route to Chaos

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 incomplete in dimensions d>1. For non-normal Jacobians, pointwise spectral stability can suggest everywhere local contraction, while non-orthogonal eigenvectors still allow transient singular-vector amplification. We construct four low-dimensional deterministic maps realizing this mechanism: partition-reinjected, phase-prescribed, feedback-driven, and affine-reinjected non-normal routes to chaos. In all cases, the instantaneous Jacobian remains spectrally stable on the attractor, with eigenvalues fixed inside the unit disk, while increasing non-normality drives the maximal Lyapunov exponent through zero. The positive exponent therefore describes sustained asymptotic chaos, not transient chaos. Across the four classes, the common signature is spectral radius $ρ_{\mathrm{traj}}^{\max}<1$, singular value $σ_{\mathrm{traj}}^{\max}>1$ maximum Lyapunov exponent $λ_1>0$, and an increase of attractor dimension. These examples identify non-normality and recurrent reinjection of transiently amplified directions as a deterministic route to chaos distinct from eigenvalue instability.

nlin.CD↗

arXiv2026

Pseudo-Coherence and Stochastic Synchronization: A Non-Normal Route to Collective Dynamics without Oscillators

Collective temporal organization in complex systems is commonly attributed to synchronization, resonance, or proximity to dynamical instabilities. Here we identify a distinct mechanism by which coherent, synchronization-like behavior can emerge in stochastic systems that are linearly stable and contain no intrinsic oscillators. The mechanism arises from non-normal pseudospectral amplification and leads to what we term pseudo-coherence: an intermittent form of collective organization characterized by transient phase alignment, broken time-reversal symmetry, positive entropy production, and drifting spectral peaks. Using a minimal overdamped stochastic model, we show that increasing non-normality drives a sharp pseudo-critical transition. Beyond a well-defined threshold, fluctuations concentrate along a dominant reaction mode, generating intermittent growth of Kuramoto-like order parameters and irreversible probability currents without eigenvalue crossings or Hopf bifurcations. Analytically, we demonstrate that pseudo-critical non-normal dynamics reshapes the imaginary pseudospectrum, amplifying slow fluctuations and producing coherent frequency bands under finite-time observation. These results identify pseudo-coherence as a new route to collective temporal organization in non-equilibrium systems, suggesting that apparent rhythms and synchronization in natural systems may arise from non-normal stochastic amplification rather than intrinsic oscillators.

nlin.AO↗

arXiv2025

Self-Similar Bridge between Regular and Critical Regions

In statistical and nonlinear systems, two qualitatively distinct parameter regions are typically identified: the regular region, characterized by smooth behavior of key quantities, and the critical region, where these quantities exhibit singularities or strong fluctuations. Due to their starkly different properties, these regions are often perceived as being weakly related, if at all. However, we demonstrate that these regions are intimately connected, a relationship that can be explicitly revealed using self-similar approximation theory. This framework enables the prediction of observable quantities near the critical point based on information from the regular region and vice versa. Remarkably, the method relies solely on asymptotic expansions with respect to a parameter, regardless of whether the expansion originates in the regular or critical region. The mathematical principles of self-similar theory remain consistent across both cases. We illustrate this connection by extrapolating from the regular region to predict the existence, location, and critical indices of a critical point of an equation of state for a statistical system, even when no direct information about the critical region is available. Conversely, we explore extrapolation from the critical to the regular region in systems with discrete scale invariance, where log-periodic oscillations in observables introduce additional complexity. Our findings provide insights and solutions applicable to diverse phenomena, including material fracture, stock market crashes, and earthquake forecasting.

cond-mat.stat-mech↗

arXiv2023

Calibration of Quantum Decision Theory: Aversion to Large Losses and Predictability of Probabilistic Choices

We present the first calibration of quantum decision theory (QDT) to a dataset of binary risky choice. We quantitatively account for the fraction of choice reversals between two repetitions of the experiment, using a probabilistic choice formulation in the simplest form without model assumption or adjustable parameters. The prediction of choice reversal is then refined by introducing heterogeneity between decision makers through their differentiation into two groups: ``majoritarian'' and ``contrarian'' (in proportion 3:1). This supports the first fundamental tenet of QDT, which models choice as an inherent probabilistic process, where the probability of a prospect can be expressed as the sum of its utility and attraction factors. We propose to parameterise the utility factor with a stochastic version of cumulative prospect theory (logit-CPT), and the attraction factor with a constant absolute risk aversion (CARA) function. For this dataset, and penalising the larger number of QDT parameters via the Wilks test of nested hypotheses, the QDT model is found to perform significantly better than logit-CPT at both the aggregate and individual levels, and for all considered fit criteria for the first experiment iteration and for predictions (second ``out-of-sample'' iteration). The distinctive QDT effect captured by the attraction factor is mostly appreciable (i.e., most relevant and strongest in amplitude) for prospects with big losses. Our quantitative analysis of the experimental results supports the existence of an intrinsic limit of predictability, which is associated with the inherent probabilistic nature of choice. The results of the paper can find applications both in the prediction of choice of human decision makers as well as for organizing the operation of artificial intelligence.

cs.AI↗

arXiv2022

Role of collective information in networks of quantum operating agents

A network of agents is considered whose decision processes are described by the quantum decision theory previously advanced by the authors. Decision making is done by evaluating the utility of alternatives, their attractiveness, and the available information, whose combinations form the probabilities to choose a given alternative. As a result of the interplay between these three contributions, the process of choice between several alternatives is multimodal. The agents interact by exchanging information, which can take two forms: (i) information that an agent can directly receive from another agent and (ii) information collectively created by the members of the society. The information field common to all agents tends to smooth out sharp variations in the temporal behaviour of the probabilities and can even remove them. For agents with short-term memory, the probabilities often tend to their limiting values through strong oscillations and, for a range of parameters, these oscillations last for ever, representing an ever lasting hesitation of the decision makers. Switching on the information field makes the amplitude of the oscillations smaller and even can halt the everlasting oscillations forcing the probabilities to converge to fixed limits. The dynamic disjunction effect is described.

physics.soc-ph↗

arXiv2018

Quantitative Predictions in Quantum Decision Theory

Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the theory of quantum measurements, which makes this approach relevant both for the description of decision making of humans and the creation of artificial quantum intelligence. General rules are formulated allowing for the explicit calculation of quantum probabilities representing the fraction of decision makers preferring the considered prospects. This provides a method to quantitatively predict decision-maker choices, including the cases of games with high uncertainty for which the classical expected utility theory fails. The approach is applied to experimental results obtained on a set of lottery gambles with gains and losses. Our predictions, involving no fitting parameters, are in very good agreement with experimental data. The use of quantum decision making in game theory is described. A principal scheme of creating quantum artificial intelligence is suggested.

physics.soc-ph↗

arXiv2017

Information Processing by Networks of Quantum Decision Makers

We suggest a model of a multi-agent society of decision makers taking decisions being based on two criteria, one is the utility of the prospects and the other is the attractiveness of the considered prospects. The model is the generalization of quantum decision theory, developed earlier for single decision makers realizing one-step decisions, in two principal aspects. First, several decision makers are considered simultaneously, who interact with each other through information exchange. Second, a multistep procedure is treated, when the agents exchange information many times. Several decision makers exchanging information and forming their judgement, using quantum rules, form a kind of a quantum information network, where collective decisions develop in time as a result of information exchange. In addition to characterizing collective decisions that arise in human societies, such networks can describe dynamical processes occurring in artificial quantum intelligence composed of several parts or in a cluster of quantum computers. The practical usage of the theory is illustrated on the dynamic disjunction effect for which three quantitative predictions are made: (i) the probabilistic behavior of decision makers at the initial stage of the process is described; (ii) the decrease of the difference between the initial prospect probabilities and the related utility factors is proved; (iii) the existence of a common consensus after multiple exchange of information is predicted. The predicted numerical values are in very good agreement with empirical data.

physics.soc-ph↗

arXiv2017

Statistics of seismic cluster durations

Using the standard ETAS model of triggered seismicity, we present a rigorous theoretical analysis of the main statistical properties of temporal clusters, defined as the group of events triggered by a given main shock of fixed magnitude m that occurred at the origin of time, at times larger than some present time t. Using the technology of generating probability function (GPF), we derive the explicit expressions for the GPF of the number of future offsprings in a given temporal seismic cluster, defining, in particular, the statistics of the cluster's duration and the cluster's offsprings maximal magnitudes. We find the remarkable result that the magnitude difference between the largest and second largest event in the future temporal cluster is distributed according to the regular Gutenberg-Richer law that controls the unconditional distribution of earthquake magnitudes. For earthquakes obeying the Omori-Utsu law for the distribution of waiting times between triggering and triggered events, we show that the distribution of the durations of temporal clusters of events of magnitudes above some detection threshold νhas a power law tail that is fatter in the non-critical regime $n<1$ than in the critical case n=1. This paradoxical behavior can be rationalised from the fact that generations of all orders cascade very fast in the critical regime and accelerate the temporal decay of the cluster dynamics.

physics.geo-ph↗

arXiv2017

Dynamic Transition in Symbiotic Evolution Induced by Growth Rate Variation

In a standard bifurcation of a dynamical system, the stationary points (or more generally attractors) change qualitatively when varying a control parameter. Here we describe a novel unusual effect, when the change of a parameter, e.g. a growth rate, does not influence the stationary states, but nevertheless leads to a qualitative change of dynamics. For instance, such a dynamic transition can be between the convergence to a stationary state and a strong increase without stationary states, or between the convergence to one stationary state and that to a different state. This effect is illustrated for a dynamical system describing two symbiotic populations, one of which exhibits a growth rate larger than the other one. We show that, although the stationary states of the dynamical system do not depend on the growth rates, the latter influence the boundary of the basins of attraction. This change of the basins of attraction explains this unusual effect of the quantitative change of dynamics by growth rate variation.

q-bio.PE↗

arXiv2017

Quantum Probabilities as Behavioral Probabilities

We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is applicable to the description of human decision making. The applicability of quantum rules for describing decision making is connected with the nontrivial process of making decisions in the case of composite prospects under uncertainty. Such a process involves deliberations of a decision maker when making a choice. In addition to the evaluation of the utilities of considered prospects, real decision makers also appreciate their respective attractiveness. Therefore, human choice is not based solely on the utility of prospects, but includes the necessity of resolving the utility-attraction duality. In order to justify that human consciousness really functions similarly to the rules of quantum theory, we develop an approach defining human behavioral probabilities as the probabilities determined by quantum rules. We show that quantum behavioral probabilities of humans not merely explain qualitatively how human decisions are made, but they predict quantitative values of the behavioral probabilities. Analyzing a large set of empirical data, we find good quantitative agreement between theoretical predictions and observed experimental data.

q-bio.NC↗

arXiv2016

Quantum decision theory in simple risky choices

Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of uncertainty and other effects that are particularly manifest in cognitive processes, which makes it well suited for the study of decision making. QDT describes a decision maker's choice as a stochastic event occurring with a probability that is the sum of an objective utility factor and a subjective attraction factor. QDT offers a prediction for the average effect of subjectivity on decision makers, the quarter law. We examine individual and aggregated (group) data, and find that the results are in good agreement with the quarter law at the level of groups. At the individual level, it appears that the quarter law could be refined in order to reflect individual characteristics. This article revisits the formalism of QDT along a concrete example and offers a practical guide to researchers who are interested in applying QDT to a dataset of binary lotteries in the domain of gains.

physics.soc-ph↗

arXiv2016

Inconclusive quantum measurements and decisions under uncertainty

We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally testable. Since the mathematical structure of Quantum Decision Theory has been developed in analogy with the theory of quantum measurements, the inconclusive quantum measurements correspond, in Quantum Decision Theory, to intermediate stages of decision making in the process of taking decisions under uncertainty. The general form of the quantum probability for a composite event is the sum of a utility factor, describing a rational evaluation of the considered prospect, and of an attraction factor, characterizing irrational, subconscious attitudes of the decision maker. Despite the involved irrationality, the probability of prospects can be evaluated. This is equivalent to the possibility of calculating quantum probabilities without specifying hidden variables. We formulate a general way of evaluation, based on the use of non-informative priors. As an example, we suggest the explanation of the decoy effect. Our quantitative predictions are in very good agreement with experimental data.

quant-ph↗

arXiv2016

Quantum probability and quantum decision making

A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary.

quant-ph↗

arXiv2015

Quantum decision making by social agents

The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social interactions, which influence the decisions of individual agents, leads to a generalization of the quantum decision theory developed earlier by the authors for separate individuals. The generalized approach is free of the standard paradoxes of classical decision theory. This approach also explains the error-attenuation effects observed for the paradoxes occurring when decision makers, who are members of a society, consult with each other, increasing in this way the available mutual information. A precise correspondence between quantum decision theory and classical utility theory is formulated via the introduction of an intermediate probabilistic version of utility theory of a novel form, which obeys the requirement that zero-utility prospects should have zero probability weights.

physics.soc-ph↗

arXiv2015

Role of information in decision making of social agents

physics.soc-ph↗