相关论文: Detecting bifurcations in dynamical systems with C…

We consider several different bidirectional Whitham equations that have recently appeared in the literature. Each of these models combine the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow…

A central challenge in hydrodynamic turbulence is identifying precisely when, and at which length scales, strong turbulent fluctuations (STFs) emerge and develop into intermittent events, which are often obscured by conventional statistical…

We show bifurcation of localized spike solutions from spatially constant states in systems of nonlocally coupled equations in the whole space. The main assumptions are a generic bifurcation of saddle-node or transcritical type for spatially…

Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…

Topological data analysis (TDA) has emerged as an effective approach in data science, with its key technique, persistent homology, rooted in algebraic topology. Although alternative approaches based on differential topology, geometric…

Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…

A one-parameter family of time-reversible systems on $\mathbb{T}^3$ is considered. It is shown that the dynamics is not conservative, namely the attractor and repeller intersect but not coincide. We explain this as the manifestation of the…

The interplay between bifurcations and random switching processes of vector fields is studied. More precisely, we provide a classification of piecewise deterministic Markov processes arising from stochastic switching dynamics near fold,…

Recurrence plots (RPs) are powerful tools for visualizing time series dynamics; however, traditional Recurrence Quantification Analysis (RQA) often relies on global metrics, such as line counting, that can overlook system-specific,…

We study a class of bifurcations generically occurring in dynamical systems with non-mutual couplings ranging from models of coupled neurons to predator-prey systems and non-linear oscillators. In these bifurcations, extended attractors…

In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even implementation. We propose a pair of methods for detecting…

The Jacobi set of a bivariate scalar field is the set of points where the gradients of the two constituent scalar fields align with each other. It captures the regions of topological changes in the bivariate field. The Jacobi set is a…

Spectral bifurcation diagrams (SBDs) have recently emerged as an efficient tool for identifying dynamical transitions in nonlinear systems through frequency-domain analysis. Previous studies have been limited to numerical investigations,…

Topological data analysis is a powerful framework for extracting useful topological information from complex datasets. Recent work has shown its application for the dynamical analysis of classical dissipative systems through a…

Local bifurcation analysis plays a central role in understanding qualitative transitions in networked nonlinear dynamical systems, including dynamic neural network and opinion dynamics models. In this article we establish explicit bounds of…

For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of their position. By assuming a global…

We investigate the topological properties of dynamical states evolving on periodic oriented graphs. This evolution, that encodes the scattering processes occurring at the nodes of the graph, is described by a single-step global operator, in…

This paper investigates the dynamical behavior of periodic solutions for a class of second-order non-autonomous differential equations. First, based on the Lyapunov-Schmidt reduction method for finite-dimensional functions, the…

We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…

Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…