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Coexistence of different dynamical phases is a hallmark of glassy dynamics. This is well-studied in classical systems where the underlying theoretical framework is that of large deviation theory. The presence of a similar phase coexistence…
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…
Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several…
Empirically observed time series in physics, biology, or medicine, are commonly generated by some underlying dynamical system (DS) which is the target of scientific interest. There is an increasing interest to harvest machine learning…
Physically motivated stochastic dynamics are often used to sample from high-dimensional distributions. However such dynamics often get stuck in specific regions of their state space and mix very slowly to the desired stationary state. This…
The paper presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to…
The oscillations observed in many time series, particularly in biomedicine, exhibit morphological variations over time. These morphological variations are caused by intrinsic or extrinsic changes to the state of the generating system,…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…
The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and…
Finding interpretable biomechanical models can provide insight into the functionality of organs with regard to physiology and disease. However, identifying broadly applicable dynamical models for in vivo tissue remains challenging. In this…
We investigate the recovery dynamics of healthy cardiac activity after physical exertion using multimodal biosignals recorded with a polycardiograph. Multifractal features derived from the singularity spectrum capture the scale-invariant…
Advances in intensity-based microscopy techniques have improved our ability to quantify particle motion at microscopic scales, enabling insight into diffusion and collective dynamics. Building on this foundation, we introduce a novel…
Highway traffic states data collected from a network of sensors can be considered a high-dimensional nonlinear dynamical system. In this paper, we develop a novel data-driven method -- anti-circulant dynamic mode decomposition with…
Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function…
Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded…
We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…