We introduce a data-driven framework that maps noisy oscillatory time series directly onto the Hopf normal form, enabling inference of underlying dynamics without knowledge of governing equations. By embedding the normal form in a probabilistic state-space model, the method jointly infers latent states and system parameters, yielding robust estimates of the natural frequency, Floquet exponent, and asymptotic phase even far from the bifurcation point and under strong noise. Combined with complex Gaussian process regression, the approach further reconstructs phase and amplitude sensitivity functions from data. Benchmarks on the van der Pol oscillator demonstrate substantially improved accuracy and noise robustness compared with existing phase-based and regression methods. This work establishes a direct bridge between normal-form theory and statistical inference, providing a general and practical route to low-dimensional descriptions of oscillatory dynamics in complex systems.
We study the reconstruction of an unknown dynamical system from a single noisy scalar time series. The goal is to recover the underlying dynamics for forecasting. We introduce a method that uses differential embedding coordinates to identify a rational closure of the embedding dynamics directly from data. The closure i...
Multi-step training of sparse, interpretable models of dynamical systems directly from time-series data yields models with accurate short-term dynamics and strong agreement in long-time statistical properties, including mean, variance, and Lyapunov exponents.
Identifying stochastic dynamical systems from observational data remains a major challenge in applied mathematics and engineering, particularly when complex systems are influenced by random perturbations and incomplete empirical information. This comprehensive review aims to examine state-of-the-art data-driven methods...
Rishav Jha, Kameshwar Sahani, S. K. Sahani et al.· African Multidisciplinary Jo...· 0 citations
Functional dependence measures have become an important tool in the analysis of nonlinear time series and are typically formulated with respect to a given innovation representation of the process. This note points out that the probability space on which such representations yield the expected memory loss properties may...
It is demonstrated that the squared Pearson correlation coefficient provides a simple quantitative criterion for distinguishing chaos from noise directly from observed time-series data.
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 d...
V. Saiprasad, V. Troude, D. Sornette· 0 citations
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