Related papers: Simple dynamics on graphs
Given a graph $G$, viewed as a loop-less symmetric digraph, we study the maximum number of fixed points in a conjunctive boolean network with $G$ as interaction graph. We prove that if $G$ has no induced $C_4$, then this quantity equals…
Understanding the topology of the state space has proven to be extremely efficient for dynamical systems with a continuous state space. On the other hand, for particle systems on finite simple graphs, it has not yet been subject to deep…
A variety of physical, social and biological systems generate complex fluctuations with correlations across multiple time scales. In physiologic systems, these long-range correlations are altered with disease and aging. Such correlated…
For a graph $G$ and an integer-valued threshold function $\tau$ on its vertex set, a dynamic monopoly is a set of vertices of $G$ such that iteratively adding to it vertices $u$ of $G$ that have at least $\tau(u)$ neighbors in it eventually…
We address the problem of computing a Minimal Dominating Set in highly dynamic distributed systems. We assume weak connectivity, i.e., the network may be disconnected at each time instant and topological changes are unpredictable. We make…
In this article, we study the large-population limit of interacting particle systems posed on weighted random graphs. In that aim, we introduce a general framework for the construction of weighted random graphs, generalizing the concept of…
Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…
This paper addresses the bipartite consensus-control problem in open multi-agent systems containing both cooperative and antagonistic interactions. In these systems, new agents can join and new interactions can be formed over time.…
Automata networks are a versatile model of finite discrete dynamical systems composed of interacting entities (the automata), able to embed any directed graph as a dynamics on its space of configurations (the set of vertices, representing…
Many dynamical systems, including thermal, fluid, and multi-agent systems, can be represented as weighted graphs. In this paper we consider whether the unstable states of such systems can be observed from limited discrete-time measurement,…
A finite collection $P$ of finite sets tiles the integers iff the integers can be expressed as a disjoint union of translates of members of $P$. We associate with such a tiling a doubly infinite sequence with entries from $P$. The set of…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
In this work we establish that finite directed graphs give rise to semiflows on the power set of their nodes. We analyze the topological dynamics for semiflows on finite directed graphs by characterizing Morse decompositions, recurrence…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
In this paper, inspired by the elegant work of Good and Meddaugh \cite{GM} and the graph models for zero-dimensional systems developed by several authors, like Gambaudo and Martens \cite{GM06}, Shimomura \cite{Sh14}. We try to discover a…
In this article, we study finite dynamical systems defined over graphs, where the functions are applied asynchronously. Our goal is to quantify and understand stability of the dynamics with respect to the update sequence, and to relate this…
The $k$-dominating graph $D_k(G)$ of a graph $G$ is defined on the vertex set consisting of dominating sets of $G$ with cardinality at most $k$, two such sets being adjacent if they differ by either adding or deleting a single vertex. A…
The dynamical properties of finite dynamical systems (FDSs) have been investigated in the context of coding theoretic problems, such as network coding, and in the context of hat games, such as the guessing game and Winkler's hat game. The…
In this paper, we introduce the notion of a dual topological graph of a given topological graph, and show that it defines a C*-algebra isomorphic to the C*-algebra of the given one. Repeating to take a dual, and taking a projective limit,…
DCOP algorithms usually rely on interaction graphs to operate. In open and dynamic environments, such methods need to address how this interaction graph is generated and maintained among agents. Existing methods require reconstructing the…