Related papers: A method to discern complexity in two-dimensional …
The last decades have not only been characterized by an explosive growth of data, but also an increasing appreciation of data as a valuable resource. Their value comes with the ability to extract meaningful patterns that are of economic,…
Correspondence identifies relationships among objects via similarities among their components; it is ubiquitous in the analysis of spatial datasets, including images, weather maps, and computational simulations. This paper develops a novel…
We investigate a lattice of coupled logistic maps where, in addition to the usual diffusive coupling, an advection term parameterized by an asymmetry in the coupling is introduced. The advection term induces periodic behavior on a…
In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy,…
Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of…
We present a quantum information-inspired framework for analyzing complex systems through multivariate time series. In this approach the system's state is encoded into a density matrix, providing a compact representation of higher-order…
Clustering bifurcations are investigated by considering models of globally coupled map lattices. Typical classes of clustering bifurcations are revealed. The clustering bifurcation thresholds of the coupled system are closely related to the…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
We introduce a new coupled map lattice model in which the weak interaction takes place via rare "collisions". By "collision" we mean a strong (possibly discontinuous) change in the system. For such models we prove uniqueness of the SRB…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
Extracting reliable indicators of chaos from a single experimental time series is a challenging task, in particular, for systems with many degrees of freedom. The techniques available for this purpose often require unachievably long time…
We propose {\delta}-MAPS, a method that analyzes spatio-temporal data to first identify the distinct spatial components of the underlying system, referred to as "domains", and second to infer the connections between them. A domain is a…
We apply a recently developed measure of multiscale complexity to the Gaussian model consisting of continuous spins with bilinear interactions for a variety of interaction matrix structures. We find two universal behaviors of the complexity…
A principled approach to cyclicality and intransitivity in paired comparison data is developed. The proposed methodology enables more precise estimation of the underlying preference profile and facilitates the identification of all cyclic…
Coupled map lattices (CMLs) are often used to study emergent phenomena in nature. It is typically assumed (unrealistically) that each component is described by the same map, and it is important to relax this assumption. In this paper, we…
We study a two-dimensional tight-binding lattice for excitons with on-site disorder, coupled to a thermal environment at infinite temperature. The disorder acts to localise an exciton spatially, while the environment generates dynamics…
Numerical simulations of coupled map lattices (CMLs) and other complex model systems show an enormous phenomenological variety that is difficult to classify and understand. It is therefore desirable to establish analytical tools 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…
It is investigated how a spatial quenched disorder modifies the dynamics of coupled map lattices. The disorder is introduced via the presence or absence of coupling terms among lattice sites. Two nonlinear maps have been considered…
A phase-separation front will leave in its wake a phase-separated morphology that differs markedly from homogeneous phase-separation morphologies. For a purely diffusive system such a front, moving with constant velocity, will generate very…