相关论文: Estimation of initial conditions from a scalar tim…

We present a method for time series analysis of both, scalar and nonscalar time-delay systems. If the dynamics of the system investigated is governed by a time-delay induced instability, the method allows to determine the delay time. In a…

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…

We propose a novel method applied to extrasolar planetary dynamics to describe the system stability. The observations in this field serve the measurements mainly of radial velocity, transit time, and/or celestial position. These scalar time…

We show that scaling arguments are very useful to analyze the dynamics of periodically modulated noisy systems. Information about the behavior of the relevant quantities, such as the signal-to-noise ratio, upon variations of the noise…

The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial…

There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the…

We consider the model reduction problem for linear time-invariant dynamical systems having nonzero (but otherwise indeterminate) initial conditions. Building upon the observation that the full system response is decomposable as a…

We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…

We provide appropriate tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions. Our approach allows for the investigation of the dependence of the largest Lyapunov exponent on various…

We develop a new approximative estimation method for conditional Shapley values obtained using a linear regression model. We develop a new estimation method and outperform existing methodology and implementations. Compared to the sequential…

We propose a reconstruction of the initial system of ordinary differential equations from a single observed variable. The suggested approach is applied to a certain class of systems which includes, in particular, the Rossler system and…

A parameter estimation method is devised for a slow-fast stochastic dynamical system, where often only the slow component is observable. By using the observations only on the slow component, the system parameters are estimated by working on…

We present the linear-stability analysis of synchronised states in coupled time-delay systems. There exists a synchronisation threshold, for which we derive upper bounds, which does not depend on the delay time. We prove that at least for…

Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…

We study systems on time scales that are generalizations of classical differential or difference equations. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of…

Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…

Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting.…

Bilinear dynamical systems are ubiquitous in many different domains and they can also be used to approximate more general control-affine systems. This motivates the problem of learning bilinear systems from a single trajectory of the…