Related papers: Periodic Source Detection in Discrete Dynamical Sy…
We propose a simple method to estimate the parameters involved in discrete dynamical systems from time series. The method is based on the concept of controlling chaos by constant feedback. The major advantages of the method are that it…
Shifting away from the traditional mass production approach, the process industry is moving towards more agile, cost-effective and dynamic process operation (next-generation smart plants). This warrants the development of control systems…
Port-Hamiltonian (pH) systems have been studied extensively for linear continuous-time dynamical systems. This manuscript presents a discrete-time pH descriptor formulation for linear, completely causal, scattering passive dynamical systems…
The method of detection of the unstable periodic spatio-temporal states of spatial extended chaotic systems has been proposed. The application of this method is illustrated by the consideration of two different systems: i) the fluid model…
It is shown that large deviation statistical quantities of the discrete time, finite state Markov process $P_{n+1}^{(j)}=\sum_{k=1}^NH_{jk}P_n^{(k)}$, where P_n^{(j)} is the probability for the j-state at the time step n and H_{jk} is the…
A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
We consider here systems with piecewise linear dynamics that are periodically sampled with a given period {\tau} . At each sampling time, the mode of the system, i.e., the parameters of the linear dynamics, can be switched, according to a…
Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…
We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for generative modeling over discrete state spaces. Rather than…
The notion of dissipative dynamical systems provides a formal description of processes that cannot generate energy internally. For these systems, changes in energy can only occur due to an external energy supply or dissipation effects.…
In this work we consider linear non-autonomous systems of Wazewski type on Hilbert spaces and provide a new approach to study their stability properties by means of a decomposition into subsystems and conditions implied on the…
This is a survey on local dynamics of holomorphic maps in one and several complex variables, discussing in particular normal forms and the structure of local stable sets in the non-hyperbolic case, and including several proofs and a vast…
Heat diffusion processes have found wide applications in modelling dynamical systems over graphs. In this paper, we consider the recovery of a $k$-bandlimited graph signal that is an initial signal of a heat diffusion process from its…
In this note, we propose a discrete model to study one-dimensional transport equations with non-local drift and supercritical dissipation. The inspiration for our model is the equation $$ \theta_t + (H\theta) \theta_x +(-\Delta)^\alpha…
We demonstrate the possibility of classifying causal systems into kinds that share a common structure without first constructing an explicit dynamical model or using prior knowledge of the system dynamics. The algorithmic ability to…
This paper proposes a fully automated method for recovering the location of a source and medium parameters in shallow waters. The scenario involves an unknown source emitting low-frequency sound waves in a shallow water environment, and a…
A causal input-output system may be described by a function space for inputs, a function space for outputs, and a causal operator mapping the input space into the output space. A particular representation of the state of such a system at…
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…
Causal discovery from observational data is an important tool in many branches of science. Under certain assumptions it allows scientists to explain phenomena, predict, and make decisions. In the large sample limit, sound and complete…