Outer-totalistic cellular automata on graphs

We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically sensitive elementary cellular automata and find that the overall number of complex patterns decreases under increasing neighborhood size in regular graphs. As exemplary applications, we apply the formalism to complex networks and compare the potential of scale-free graphs and metabolic networks to generate complex dynamics.Comment: 5 pages, 4 figures, 1 table. To appear in Physics Letters

Similar impact of topological and dynamic noise on complex patterns

Shortcuts in a regular architecture affect the information transport through the system due to the severe decrease in average path length. A fundamental new perspective in terms of pattern formation is the destabilizing effect of topological perturbations by processing distant uncorrelated information, similarly to stochastic noise. We study the functional coincidence of rewiring and noisy communication on patterns of binary cellular automata.Comment: 8 pages, 7 figures. To be published in Physics Letters

The Regularizing Capacity of Metabolic Networks

Despite their topological complexity almost all functional properties of metabolic networks can be derived from steady-state dynamics. Indeed, many theoretical investigations (like flux-balance analysis) rely on extracting function from steady states. This leads to the interesting question, how metabolic networks avoid complex dynamics and maintain a steady-state behavior. Here, we expose metabolic network topologies to binary dynamics generated by simple local rules. We find that the networks' response is highly specific: Complex dynamics are systematically reduced on metabolic networks compared to randomized networks with identical degree sequences. Already small topological modifications substantially enhance the capacity of a network to host complex dynamic behavior and thus reduce its regularizing potential. This exceptionally pronounced regularization of dynamics encoded in the topology may explain, why steady-state behavior is ubiquitous in metabolism.Comment: 6 pages, 4 figure

A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat

Critical phenomena in cellular automata: perturbing the update, the transitions, the topology

International audienceWe survey the effect of perturbing the regular structure of a cellular automaton. We are interested in critical phenomena, i.e., when a continuous variation in the local rules of a cellular automaton triggers a qualitative change of its global behaviour. We focus on three types of perturbations: (a) when the updating is made asynchronous, (b) when the transition rule is made stochastic, (c) when the topological defects are introduced. It is shown that although these perturbations have various effects on CA models, they generally produce the same effects, which are identified as first-order or second-order phase transitions. We present open questions related to this topic and discuss implications on the activity of modelling

Dynamical behavior and influence of stochastic noise on certain generalized Boolean networks

This study considers a simple Boolean network with N nodes, each node’s state at time t being determined by a certain number of parent nodes. The network is analyzed when the connectivity k is fixed or variable. Making use of a Boolean rule that is a generalization of Rule 22 of elementary cellular automata, a generalized formula for providing the probability of finding a node in state 1 at a time t is determined. We show typical behaviors of the iterations, and we study the dynamics of the network through Lyapunov exponents, bifurcation diagrams, and fixed point analysis. We conclude that the network may exhibit stability or chaos depending on the underlying parameters. In general high connectivity is associated with a convergence to zero of the probability of finding a node in state 1 at time t. We also study analytically and numerically the dynamics of the network under a stochastic noise procedure. We show that under a smaller probability of disturbing the nodes through the noise procedure the system tends to exhibit more nodes in the same state. For many parameter combinations there is no critical value of the noise parameter below which the network remains organized and above which it behaves randomly

Complex systems dynamics in laser excited ensembles of Rydberg atoms

In this thesis I present experimental and theoretical results showing that an ultracold gas under laser excitation to Rydberg states offers a controllable platform for studying the interesting complex dynamics that can emerge in driven-dissipative systems. The findings can be summarized according to the following three main insights: (i) The discovery of self-organized criticality (SOC) in our Rydberg system under facilitated excitation via three signatures: self-organization of the density to a stationary state; scale invariant behavior; and a critical response in terms of power-law distributed excitation avalanches. Additionally, we explore a mechanism inherent to our system which stabilizes the SOC state. We further investigate this stabilization via a controlled, variable driving of the system. These analyses can help answer the question of why scale invariant behavior is so prevalent in nature. (ii) A striking connection between the power-law growth of the Rydberg excitation number and epidemic spreading is found. Based on this, an epidemic network model is devised which efficiently describes the collective excitation dynamics. The importance of heterogeneity in the emergent Rydberg network and associated Griffiths effects provide a way to explain the observation of non-universal power laws. (iii) A novel quantum cellular automata implementation is proposed using atomic arrays together with multifrequency laser fields. This provides a natural framework to study the relation between microscopic processes and global dynamics, where special rules are found to generate entangled states with applications in quantum metrology and computing

Predictability: a way to characterize Complexity

Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a characterization of the unpredictability of a system gives a measure of its complexity. Adopting this point of view, we review some developments in the characterization of the predictability of systems showing different kind of complexity: from low-dimensional systems to high-dimensional ones with spatio-temporal chaos and to fully developed turbulence. A special attention is devoted to finite-time and finite-resolution effects on predictability, which can be accounted with suitable generalization of the standard indicators. The problems involved in systems with intrinsic randomness is discussed, with emphasis on the important problems of distinguishing chaos from noise and of modeling the system. The characterization of irregular behavior in systems with discrete phase space is also considered.Comment: 142 Latex pgs. 41 included eps figures, submitted to Physics Reports. Related information at this http://axtnt2.phys.uniroma1.i