Related papers: Detecting Regime Transitions in Dynamical Systems …

We present a general and flexible framework for detecting regime changes in complex, non-stationary data across multi-trial experiments. Traditional change point detection methods focus on identifying abrupt changes within a single time…

Many natural systems undergo critical transitions, i.e. sudden shifts from one dynamical regime to another. In the climate system, the atmospheric boundary layer can experience sudden transitions between fully turbulent states and…

Analyzing when noisy trajectories, in the two dimensional plane, of a stochastic dynamical system exit the basin of attraction of a fixed point is specifically challenging when a periodic orbit forms the boundary of the basin of attraction.…

Machine learning approaches have been widely used for discovering the underlying physics of dynamical systems from measured data. Existing approaches, however, still lack robustness, especially when the measured data contain a large level…

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…

A wide variety of physical systems ranging from the firing of neurons to eutrophication of lakes to the presence of Arctic summer sea ice exhibit a phenomenon known as tipping. In mathematical models, tipping can be caused by bifurcations,…

Regime switching is ubiquitous in many complex dynamical systems with multiscale features, chaotic behavior, and extreme events. In this paper, a causation entropy boosting (CEBoosting) strategy is developed to facilitate the detection of…

Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…

We develop a mixture procedure for multi-sensor systems to monitor data streams for a change-point that causes a gradual degradation to a subset of the streams. Observations are assumed to be initially normal random variables with known…

Motivated by the normal form of a fast-slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an application of the explicit Euler method. Tracking…

In this paper, a new combination of a dynamic transformation method and a trajectory-based integration technique is proposed for the model independent computation of unstable equilibrium points (UEPs). The transformation method converts a…

We present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of a new iterative scheme and an effective technique for selecting initial points. The iterative…

Persistent entropy (PE) is an information-theoretic summary statistic of persistence barcodes that has been widely used to detect regime changes in complex systems. Despite its empirical success, a general theoretical understanding of when…

Most complex systems are intrinsically dynamic in nature. The evolution of a dynamic complex system is typically represented as a sequence of snapshots, where each snapshot describes the configuration of the system at a particular instant…

The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is…

Characterizing conformational transitions in physical systems remains a fundamental challenge, as traditional sampling methods struggle with the high-dimensional nature of molecular systems and high-energy barriers between stable states.…

Dynamical systems in the life sciences are often composed of complex mixtures of overlapping behavioral regimes. Cellular subpopulations may shift from cycling to equilibrium dynamics or branch towards different developmental fates. The…

We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…

An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp.~6172--6175], which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.~4733--4736]…

An algorithm for detecting unstable periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp. 6172-6175] which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.…