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We conduct a series of experiments designed to empirically demonstrate the effects of varying the structural features of a multi-agent emergent communication game framework. Specifically, we model the interactions (edges) between individual…
We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the…
Flow networks can describe many natural and artificial systems. We present a model for a flow system that allows for volume accumulation, includes conduits with a non-linear relation between current and pressure difference, and can be…
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
Progress in the creation of large scale, artificial quantum coherent structures demands the investigation of their nonequilibrium dynamics when strong interactions, even between remote parts, are non-perturbative. Analysis of multiparticle…
Various natural and engineered systems, from urban traffic flow to the human brain, can be described by large-scale networked dynamical systems. These systems are similar in being comprised of a large number of microscopic subsystems, each…
We consider large-dimensional dynamical systems involving a linear force and a random force comprising both potential and non-conservative contributions. Such systems are known to exhibit a topological trivialization phase transition as the…
Random substitutions are a natural generalisation of their classical `deterministic' counterpart, whereby at every step of iterating the substitution, instead of replacing a letter with a predetermined word, every letter is independently…
Coupled excitable systems can generate a variety of patterns. In this work, we investigate coupled Chialvo maps in two dimensions under two types of nearest-neighbor couplings. One coupling produces ringlike patterns, while the other…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
There are rich emergent phase behaviors in non-equilibrium active systems. Flocking and clustering are two representative dynamic phases. The relationship between these two phases is still unclear. In the paper, we numerically investigate…
We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…
Control schemes for dynamical systems typically involve stabilizing unstable periodic orbits. In this paper we introduce a new paradigm of control that involves `trapping' the dynamics arbitrarily close to any desired trajectory. This is…
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics…
The Poincar\'e map is widely used to study the qualitative behavior of dynamical systems. For instance, it can be used to describe the existence of periodic solutions. The Poincar\'e map for dynamical systems with impulse effects was…
This paper is a first step in the study of the recurrence behavior in random dynamical systems and randomly perturbed dynamical systems. In particular we define a concept of quenched and annealed return times for systems generated by the…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degreegrowth of these iterations. We use these estimates to bound exponential sums along the orbits of these dynamical…
In this paper, we investigate the dynamics on the hyperspace induced by a non-autonomous dynamical system $(X,\mathbb{F})$, where the non-autonomous system is generated by a sequence $(f_n)$ of continuous self maps on $X$. We relate the…