Related papers: Nagumo-Type Characterization of Forward Invariance…
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…
The objective of this work is to examine the integrability of Hamiltonian systems in $2D$ spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability.…
We present a stability analysis for two different rotational pressure correction schemes with open and traction boundary conditions. First, we provide a stability analysis for a rotational version of the grad-div stabilized scheme of [A.…
We deal with monotone inclusion problems of the form $0\in Ax+Dx+N_C(x)$ in real Hilbert spaces, where $A$ is a maximally monotone operator, $D$ a cocoercive operator and $C$ the nonempty set of zeros of another cocoercive operator. We…
Multiplicity of phase states within frequency locked bands in periodically forced oscillatory systems may give rise to front structures separating states with different phases. A new front instability is found within bands where…
Nested conditions are used, among other things, as a graphical way to express first order formulas ruling the applicability of a graph transformation rule to a given match. In this paper, we propose (for the first time) a notion of…
This paper presents a constraint-enforcing control framework for a class of discrete-time strict-feedback nonlinear systems. The objective is to guarantee closed-loop stability while ensuring forward invariance of a prescribed safe set…
A method for certifying exact input trackability for constrained discrete time linear systems is introduced in this paper. A signal is assumed to be drawn from a reference set and the system must track this signal with a linear combination…
This paper concerns an inverse problem for the initial boundary value problem of the two-dimensional Navier-Stokes system defined in a bounded simply connected domain with slip, vorticity boundary conditions, and a global vorticity…
Recent advances in latent diffusion models have demonstrated state-of-the-art performance in high-dimensional time-series data synthesis while providing flexible control through conditioning and guidance. However, existing methodologies…
We study the boundary contribution to the low energy effective action of the open string describing the confining flux tube in gauge theories. The form of the boundary terms is strongly constrained by the requirement of Lorentz symmetry,…
Conventional deep learning prioritizes unconstrained optimization, yet biological systems operate under strict metabolic constraints. We propose that these physical constraints shape dynamics to function not as limitations, but as a…
An investigation of dynamical chiral symmetry breaking on the light front is made in the Nambu--Jona-Lasinio model with one flavor and N colors. Analysis of the model suffers from extraordinary complexity due to the existence of a…
While invariant measures are widely employed to analyze physical systems when a direct study of pointwise trajectories is intractable, e.g., due to chaos or noise, they cannot uniquely identify the underlying dynamics. Our first result…
New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of…
In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…
In this paper, we study abstract dynamical systems with discrete phase spaces. One example of such a system is induced by the $3 x{+}1$-map on the set of all natural numbers, also known as the Collatz map. Our main focus is on dynamical…
The paper addresses the formulation and analysis of direct and inverse problems for a Langevin-type fractional differential equation under a non-local condition imposed on the time variable. An additional condition for solving the inverse…
This paper focuses on a class of additive perturbations in dynamical systems. An equivalence statement for this construction is discovered, and consequently, a method of checking a notion of positive invariance with perturbation. The…
Invariant sets define regions of the state space where system constraints are always satisfied. The majority of numerical techniques for computing invariant sets have been developed for discrete-time systems with a fixed sampling time.…