Related papers: Linear Invariants for Linear Systems
In order to study the invariant measures of discrete KdV- and Toda-type systems, this article focusses on models, discretely indexed in space and time, whose dynamics are deterministic and defined locally via lattice equations. A detailed…
We classify quasilinear systems in Riemann invariants whose characteristic webs are linearizable on every solution. Although the linearizability of an individual web is a rather nontrivial differential constraint, the requirement of…
The paper intends to offer a general overview on what the concept of integrability means for a nonlinear dynamical system and how the symmetry method can be applied for approaching it. After a general part where key problems as direct and…
We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearity-induced coupling of the linearization's…
Standard Bayesian approaches for linear time-invariant (LTI) system identification are hindered by parameter non-identifiability; the resulting complex, multi-modal posteriors make inference inefficient and impractical. We solve this…
Linearizability is the de facto consistency condition for concurrent objects, widely used in theory and practice. Loosely speaking, linearizability classifies concurrent executions as correct if operations on shared objects appear to take…
The analysis of the time evolution of unstable states which are linear superposition of other, observable, states can, in principle, be carried out in two distinct, non-equivalent ways. One of the methods, usually employed for the neutral…
A linear inference is a valid inequality of Boolean algebra in which each variable occurs at most once on each side. In this work we leverage recently developed graphical representations of linear formulae to build an implementation that is…
Termination analysis of linear loops plays a key r\^{o}le in several areas of computer science, including program verification and abstract interpretation. Already for the simplest variants of linear loops the question of termination…
In this paper, we investigate delayed linear difference systems and establish several fundamental results. We first provide a Kalman-type rank condition tailored for delayed linear difference systems. Furthermore, we construct the discrete…
Linear response theory is a fundamental framework studying the macroscopic response of a physical system to an external perturbation. This paper focuses on the rigorous mathematical justification of linear response theory for Langevin…
We generalize two embedding theorems and investigate the existence and multiplicity of nontrivial solutions for a $(p,q)$-Laplacian coupled system with perturbations and two parameters $\lambda_1$ and $\lambda_2$ on locally finite graph. By…
Systems whose variable are constrained to be positive allow computationally efficient control design. We generalize these results to linear systems which leave a cone invariant. This is a wider class of systems than positive systems. We…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
Linear optics (LO) prohibits certain transformations. In this paper, we study the conditions for a computation to be possible in LO. We find that there are finitely many polynomials such that each of these polynomials evaluates to the same…
We present a new version of the Grobman-Hartman's linearization theorem for random dynamics. Our result holds for infinite dimensional systems whose linear part is not necessarily invertible. In addition, by adding some restrictions on the…
We propose an abstract approach to prove local uniqueness and conditional H\"older stability to non-linear inverse problems by linearization. The main condition is that, in addition to the injectivity of the linearization $A$, we need a…
Complex systems typically have many different parts and facets, with different characteristics. In a multi-paradigm approach to modeling, formalisms with different natures are used in combination to describe complementary parts and aspects…
We consider the Li\'enard equation and we give a sufficient condition to ensure existence and uniqueness of limit cycles. We compare our result with some other existing ones and we give some applications.
It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…