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A class of models of driven diffusive systems which is shown to exhibit phase separation in $d=1$ dimensions is introduced. Unlike all previously studied models exhibiting similar phenomena, here the phase separated state is fluctuating in…
In this exploratory paper we introduce the problem of cognitive agents that learn how to modify their environment according to local sensing to reach a global goal. We concentrate on discrete dynamics (cellular automata) on a…
We have determined families of two-dimensional deterministic totalistic cellular automaton rules whose stationary density of active sites exhibits a period two in time. Each family of deterministic rules is characterized by an ``average…
Cellular renewing active matter - assemblies of proliferating and apoptotic cells - underlies tissue homeostasis, morphogenesis, and clonal competition. Previous work in one-dimensional periodic systems identified a fitness advantage…
We present a probabilistic cellular automaton with two absorbing states, which can be considered a natural extension of the Domany-Kinzel model. Despite its simplicity, it shows a very rich phase diagram, with two second-order and one…
Some deterministic cellular automata have been observed to follow the pattern of the second law of thermodynamics: starting from a partially disordered state, the system evolves towards a state of equilibrium characterized by maximal…
Many types of spatiotemporal patterns have been observed under nonequilibrium conditions. Cycling through four or more states can provide specific dynamics, such as the spatial coexistence of multiple phases. However, transient dynamics…
We examine the depinning and driven dynamics of a system in which there is a competition between long range Coulomb repulsive and short range attractive interactions. In the absence of disorder the system forms Wigner crystal, stripe, and…
A necessary and sufficient condition for a one-dimensional q-state n-input cellular automaton rule to be number-conserving is established. Two different forms of simpler and more visual representations of these rules are given, and their…
The problem of competitive nucleation in the framework of Probabilistic Cellular Automata is studied from the dynamical point of view. The dependence of the metastability scenario on the self--interaction is discussed. An intermediate…
We review recent progress on the statiscal physics study of the problem of coloring random graphs with q colors. We discuss the existence of a threeshold at connectivity c_q=2q log q-log q-1+o(1) separting two phases which are respectivily…
The physical regions (domains or basins) within the molecular structure are open systems that exchange charge between them and consequently house a fractional number of electrons (net charge). The natural framework describing the quantum…
We consider a stochastic model, describing the growth of two competing infections on $\mathbb{R}^d$. The growth takes place by way of spherical outbursts in the infected region, an outburst in the type 1 (2) infected region causing all…
This article is dedicated to the study and comparison of two chemostat-like competition models in a heterogeneous environment. The first model is a probabilistic model where we build a PDMP simulating the effect of the temporal…
We present a picture of phase transitions of the system with colored multiplicative noise. Considering the noise amplitude as the power-law dependence of the stochastic variable $x^a$ we show the way to phase transitions disorder-order and…
We study the evolution of recombination using a microscopic model developed within the frame of the theory of quantitative traits. Two components of fitness are considered: a static one that describes adaptation to environmental factors not…
In the present chapter we study the emergence of global patterns in large groups in first and second-order multi-agent systems, focusing on two ingredients that influence the dynamics: the interaction network and the state space. The state…
A new kind of cellular automaton (CA) for the study of the dynamics of urban systems is proposed. The state of a cell is not described using a finite set, but by means of continuum variables. A population sector is included, taking into…
A deterministic system of interacting agents is considered as a model for economic dynamics. The dynamics of the system is described by a coupled map lattice with near neighbor interactions. The evolution of each agent results from the…
The classical game of rock-paper-scissors have inspired experiments and spatial model systems that address robustness of biological diversity. In particular the game nicely illustrates that cyclic interactions allow multiple strategies to…