Related papers: A Dynamical Microscope for Multivariate Oscillator…

The paper algorithmizes the problem of regime change point identification for data measured in a system exhibiting impulsive behaviors. This is a fundamental challenge for annotation of measurement data relevant, e.g., for designing…

The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

In this work, we investigate a model of an adaptive networked dynamical system, where the coupling strengths among phase oscillators coevolve with the phase states. It is shown that in this model the oscillators can spontaneously…

We introduce a notion of emergence for coarse-grained macroscopic variables associated with highly-multivariate microscopic dynamical processes, in the context of a coupled dynamical environment. Dynamical independence instantiates the…

Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, and engineering…

In this work, we introduce a generalized framework for multiscale state-space modeling that incorporates nested nonlinear dynamics, with a specific focus on Bayesian learning under switching regimes. Our framework captures the complex…

Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…

We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…

By characterizing the phase dynamics in coupled oscillators, we gain insights into the fundamental phenomena of complex systems. The collective dynamics in oscillatory systems are often described by order parameters, which are insufficient…

Dynamical systems, that are used to model power grids, the brain, and other physical systems, can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may…

Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…

The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…

The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…

It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong…

Nonlinear dynamical systems with regime transitions are typically described by ordinary differential equations with jumping parameters parameters. Traditional methods often treat change-point detection and parameter estimation as separate…

Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

Singularities in macroscopic systems at discontinuous phase transitions are replaced in finite systems by sharp but continuous changes. Both the energy differences between metastable and stable phases and the energy barriers separating…

Many biological systems evolve through continuous local dynamics while switching between latent regimes defined by learning, stimulus context, internal state, or developmental stage. These processes are often observed only as unpaired…