Related papers: Random Time Dynamical Systems
We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various timescales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis…
In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these…
Encoding a sequence of observations is an essential task with many applications. The encoding can become highly efficient when the observations are generated by a dynamical system. A dynamical system imposes regularities on the observations…
Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…
In the first part of this paper, we consider a family of continuous-time dynamical systems coupled with diffusion-transmutation processes. Under certain conditions, such randomly perturbed dynamical systems can be interpreted as an averaged…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
This paper develops a set of simplified dynamical models with which to explore the conditions under which temporal differentiation leads to optimized system output. By temporal differentiation, we mean a division of labor whereby different…
We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…
Dynamics with choice is a generalization of discrete-time dynamics where instead of the same evolution operator at every time step there is a choice of operators to transform the current state of the system. This notion is new and…
We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in thermodynamics, which are idealized processes where…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
Dynamics, the physical change in time and a pillar of natural sciences, can be regarded as an emergent phenomenon when the system of interest is part of a larger, static one. This "relational approach to time", in which the system's…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…