Related papers: Multivariate phase space reconstruction by nearest…
Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables.…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
We present a study dealing with a novel phase reconstruction method based on iterated Hilbert transform embeddings. We show results for the Stuart-Landau oscillator observed by generic observables. The benefits for reconstruction of the…
The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…
Features of the Jacobian matrix of the delay coordinates map are exploited for quantifying the robustness and reliability of state and parameter estimations for a given dynamical model using an observed time series. Relevant concepts of…
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…
Man-made environments typically comprise planar structures that exhibit numerous geometric relationships, such as parallelism, coplanarity, and orthogonality. Making full use of these relationships can considerably improve the robustness of…
Covariant phase space quantization attempts to quantize the full space of classical solutions, leading to a quantum theory in which the usual time coordinate is missing. In this paper we explore how the time evolution of the quantum states…
In this paper, we develop a novel phase retrieval approach to reconstruct x-ray differential phase shift induced by an object. A primary advantage of our approach is a higher-order accuracy over that with the conventional linear…
Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-differential equation as an ordinary…
This paper shows how to compute, for probabilistic hybrid systems, the clock approximation and linear phase-portrait approximation that have been proposed for non probabilistic processes by Henzinger et al. The techniques permit to define a…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…
It was recently shown that the phase retrieval imaging of a sample can be modeled as a simple convolution process. Sometimes, such a convolution depends on physical parameters of the sample which are difficult to estimate a priori. In this…
In this work we propose an objective function to guide the search for a state space reconstruction of a dynamical system from a time series of measurements. This statistics can be evaluated on any reconstructed attractor, thereby allowing a…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
A method to synchronize two chaotic systems with anticipation or lag, coupled in the drive response mode, is proposed. The coupling involves variable delay with three time scales. The method has the advantage that synchronization is…
A new method is proposed which allows a reconstruction of time series based on higher order multiscale statistics given by a hierarchical process. This method is able to model the time series not only on a specific scale but for a range of…
In this note, analysis of time delay systems using Lambert W function approach is reassessed. A common canonical form of time delay systems is defined. We extended the recent results of [6] for second order into nth order system. The…
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…