Related papers: Profiles of dynamical systems and their algebra
We identify many new solvable subcases of the general dynamical system characterized by two autonomous first-order ordinary differential equations with purely quadratic right-hand sides; the solvable character of these dynamical systems…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a…
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
Inspired by rational canonical forms, we introduce and analyze two decompositions of dynamic programming (DP) problems for systems with linear dynamics. Specifically, we consider both finite and infinite horizon DP problems in which the…
Connections between partial dynamcial systems, a generalized notion of partial dynamical systems defined by nested sequences of partial homeomorphisms, and triangular AF algebras which admit an integer-valued cocycle are established.
Sofic shifts are symbolic dynamical systems defined by the set of bi-infinite sequences on an edge-labeled directed graph, called a presentation. We study the computational complexity of an array of natural decision problems about…
We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…
In this document, some structured operator approximation theoretical methods for system identification of nearly eventually periodic systems, are presented. Let $\mathbb{C}^{n\times m}$ denote the algebra of $n\times m$ complex matrices.…
After investigating by examples the unusual and striking elementary properties of the Penrose tilings and the Arnold cat map, we associate a finite symbolic dynamics with finite grammar rules to each of them. Instead of studying these…
Endowing the set of functional graphs (FGs) with the sum (disjoint union of graphs) and product (standard direct product on graphs) operations induces on FGs a structure of a commutative semiring R. The operations on R can be naturally…
In this paper, we consider an extended concept of invariant for polynomial dynamical system (PDS) with domain and initial condition, and establish a sound and complete criterion for checking semi-algebraic invariants (SAI) for such PDSs.…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
An n dimensional monomial dynamical system over a finite field K is a nonlinear deterministic time discrete dynamical system with the property that each of the n component functions is a monic nonzero monomial function in n variables. In…
In a Hilbert framework, we introduce continuous and discrete dynamical systems which aim at solving inclusions governed by structured monotone operators $A=\partial\Phi+B$, where $\partial\Phi$ is the subdifferential of a convex lower…
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…
Let $\mathbf{K}$ be a field and $\phi$, $\mathbf{f} = (f_1, \ldots, f_s)$ in $\mathbf{K}[x_1, \dots, x_n]$ be multivariate polynomials (with $s < n$) invariant under the action of $\mathcal{S}_n$, the group of permutations of $\{1, \dots,…
Input-affine dynamical systems often arise in control and modeling scenarios, such as the data-driven case when state-derivative observations are recorded under bounded noise. Common tasks in system analysis and control include optimal…
In this paper we report a few examples of algebraically solvable dynamical systems characterized by 2 coupled Ordinary Differential Equations which read as follows: x_n = P(n) (x1, x2) , n = 1, 2 , with P(n) (x1, x2) specific polynomials of…