Related papers: Modeling diffusion of innovations with probabilist…
We consider the typical asymptotic behaviour of cellular automata of higher dimension (greater than 2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
We study the dynamics of the adoption of new products by agents with continuous opinions and discrete actions (CODA). The model is such that the refusal in adopting a new idea or product is increasingly weighted by neighbor agents as…
Let us consider the simplest model of one-dimensional probabilistic cellular automata (PCA). The cells are indexed by the integers, the alphabet is {0, 1}, and all the cells evolve synchronously. The new content of a cell is randomly…
Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing…
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
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…
Probabilistic Cellular Automata (PCA) are simple models used to study dynamical phase transitions. There exist mean field approximations to PCA that can be shown to exhibit a phase transition. We introduce a model interpolating between a…
In this paper, we propose a two-layer adoption-opinion model to study the diffusion of two competing technologies within a population whose opinions evolve under social influence and adoption-driven feedback. After adopting one technology,…
Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the…
Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…
We propose a stochastic model describing a process of awareness, evaluation and decision-making by agents on the d-dimensional integer lattice. Each agent may be in any of the three states belonging to the set {0, 1, 2}. In this model 0…
Cellular automata are widely used to model natural or artificial systems. Classically they are run with perfect synchrony, i.e., the local rule is applied to each cell at each time step. A possible modification of the updating scheme…
We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
A new class of automata networks is defined. Their evolution rules are determined by a probability measure p on the set of all integers Z and an indicator function I_A on the interval [0,1]. It is shown that any cellular automaton rule can…
Empirical data on the dynamics of human face-to-face interactions across a variety of social venues have recently revealed a number of context-independent structural and temporal properties of human contact networks. This universality…
A fundamental feature for understanding the diffusion of innovations through a social group is the manner in which we are influenced by our own social interactions. It is usually assumed that only direct interactions, those that form our…
The diffusion of innovations is an important topic for the consumer markets. Early research focused on how innovations spread on the level of the whole society. To get closer to the real world scenarios agent based models (ABM) started…