Related papers: Cluster dynamics in systems with constant mean fie…
Some models of clustering processes are formulated and analytically solved employing generating functions methods. Those models include events which result from combined action of the coagulation and fragmentation processes. Fragmentation…
In several environmental applications data are functions of time, essentially con- tinuous, observed and recorded discretely, and spatially correlated. Most of the methods for analyzing such data are extensions of spatial statistical tools…
This paper introduces a novel approach of clustering, which is based on group consensus of dynamic linear high-order multi-agent systems. The graph topology is associated with a selected multi-agent system, with each agent corresponding to…
We study an oscillatory medium with a nonlinear global coupling that gives rise to a harmonic mean-field oscillation with constant amplitude and frequency. Two types of cluster states are found, each undergoing a symmetry-breaking…
Using high precision Monte Carlo simulations and a mean-field theory, we explore coarsening phenomena in a simple driven diffusive system. The model is reminiscent of vehicular traffic on a two-lane ring road. At sufficiently high density,…
Apart from the role the clustering coefficient plays in the definition of the small-world phenomena, it also has great relevance for practical problems involving networked dynamical systems. To study the impact of the clustering coefficient…
Two-dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood. The action of the neighborhood on individual maps can be implemented in terms of "causal"…
We propose an entanglement mean field theory inspired approach for dealing with interacting classical many-body systems. It involves a coarse-graining technique that terminates a step before the mean field theory: While mean field theory…
Spectral Method is a commonly used scheme to cluster data points lying close to Union of Subspaces by first constructing a Random Geometry Graph, called Subspace Clustering. This paper establishes a theory to analyze this method. Based on…
It was recently shown how graphs can be used to provide descriptions of psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could fall into a sudden depression. To…
In 1961 Herbert Simon and Albert Ando published the theory behind the long-term behavior of a dynamical system that can be described by a nearly uncoupled matrix. Over the past fifty years this theory has been used in a variety of contexts,…
We extend the concept of generalized synchronization of chaos, a phenomenon that occurs in driven dynamical systems, to the context of autonomous spatiotemporal systems. It means a situation where the chaotic state variables in an…
Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a…
The collective behavior of a coupled map lattice having {\it unbounded} chaotic local dynamics is investigated through the properties of its mean field. The presence of unstable periodic orbits in the local maps determines the emergence of…
The dynamic behavior of cluster algorithms is analyzed in the classical mean field limit. Rigorous analytical results below $T_c$ establish that the dynamic exponent has the value $z_{sw}=1$ for the Swendsen-Wang algorithm and $z_{uw}=0$…
The phenomenon of synchronization occurring in a locally coupled map lattice subject to an external drive is compared to the synchronization process in an autonomous coupled map system with similar local couplings plus a global interaction.…
Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices. We expand upon recent results in spectral analysis for…
An array system of coupled maps is proposed as a model for economy evolution. The local dynamics of each map or agent is controlled by two parameters. One of them represents the growth capacity of the agent and the other one is a control…
Different collective behaviors emerging from the unknown have been examined in networks of mobile agents in recent years. Mobile systems, far from being limited to modeling and studying various natural and artificial systems in motion and…
In this paper, we utilize event-triggered coupling configuration to realize synchronization of linearly coupled dynamical systems. Here, the diffusion couplings are set up from the latest observations of the nodes of its neighborhood and…