Related papers: Switched server systems whose parameters are norma…
Switched server systems are mathematical models of manufacturing, traffic and queueing systems that have being studied since the early 1990s. In particular, it is known that typically the dynamics of such systems is asymptotically periodic:…
The review presents a parameter switching algorithm and his applications which allows numerical approximation of any attractor of a class of continuous-time dynamical systems depending linearly on a real parameter. The considered classes of…
Iterated function systems (IFSs) and their attractors have been central to the theory of fractal geometry almost from its inception. And contractivity of the functions in the IFS has been central to the theory of iterated functions systems.…
We consider a model inspired by compatibility constraints that arise between tasks and servers in data centers, cloud computing systems and content delivery networks. The constraints are represented by a bipartite graph or network that…
We study the attractor of Iterated Function Systems composed of infinitely many affine, homogeneous maps. In the special case of second generation IFS, defined herein, we conjecture that the attractor consists of a finite number of…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
In a previous paper we considered a sequence of maps on a complete metric space $(X,d)$ and derived an extension of the Banach fixed point theorem. We showed that backward trajectories of maps $X\to X$ converge under mild conditions and…
We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…
This paper considers a network of infinite-server queues with the special feature that, triggered by specific events, the network population vector may undergo a linear transformation (a `multiplicative transition'). For this model we…
We give a systematic account of iterated function systems (IFS) of weak contractions of different types (Browder, Rakotch, topological). We show that the existence of attractors and asymptotically stable invariant measures, and the validity…
Properties of the phase space of the standard map with memory are investigated. This map was obtained from a kicked fractional differential equation. Depending on the value of the parameter of the map and the fractional order of the…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
A fundamental problem in distributed computing is the distribution of requests to a set of uniform servers without a centralized controller. Classically, such problems are modeled as static balls into bins processes, where $m$ balls (tasks)…
We consider the iterated function systems (IFSs) that consist of three general similitudes in the plane with centres at three non-collinear points, and with a common contraction factor $\la\in(0,1)$. As is well known, for $\la=1/2$ the…
We consider a 2D system that models the nematic liquid crystal flow through the Navier--Stokes equations suitably coupled with a transport-reaction-diffusion equation for the averaged molecular orientations. This system has been proposed as…
This paper presents a simple periodic parameter-switching method which can find any stable limit cycle that can be numerically approximated in a generalized Duffing system. In this method, the initial value problem of the system is…
This work studies queues in a Euclidean space. Consider $N$ servers that are distributed uniformly in $[0,1]^d$. Customers arrive at the servers according to independent stationary processes. Upon arrival, they probabilistically decide…
We study a multi-server model with $n$ flexible servers and $n$ queues, connected through a bipartite graph, where the level of flexibility is captured by the graph's average degree, $d_n$. Applications in content replication in data…
Modeling the dynamics of biological networks introduces many challenges, among them the lack of first principle models, the size of the networks, and difficulties with parameterization. Discrete time Boolean networks and related continuous…
In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these…