Related papers: Localisation in a growth model with interaction
Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or…
Innovation is the driving force of human progress. Recent urn models reproduce well the dynamics through which the discovery of a novelty may trigger further ones, in an expanding space of opportunities, but neglect the effects of social…
A simple, discrete, parametric model is proposed to describe conditional (correlated) deposition of particles on a surface and formation of a connecting (percolating) cluster. The surface changes spontaneously its properties (phase…
Biological transport networks adapt through dynamic interactions between material transport and structural modification during growth and development. In this work, we present a model of transport network growth driven by local material…
Individual participants in human society collectively exhibit aggregation behavior. In this study, we present a simple microscopic model of labor force migration based on the active Brownian particles framework. In particular, agent-based…
Source-sink systems are metapopulations of patches that can be of variable habitat quality. They can be seen as graphs, where vertices represent the patches, and the weighted oriented edges give the probability of dispersal from one patch…
This paper is mainly devoted to lay an empirical foundation for further research on complex spatial dynamics of two-population interaction. Based on the US population census data, a rural and urban population interaction model is developed.…
We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the…
Cluster growth in a coagulating system of active particles (such as microswimmers in a solvent) is studied by theory and simulation. In contrast to passive systems, the net velocity of a cluster can have various scalings dependent on the…
We describe a simple spatial model of urban growth for systems of cities at the macroscopic scale, which combines direct interaction between cities and an indirect effect of physical network flows as population growth drivers. The model is…
Dynamics of two particles with short range repulsive or attractive interaction is studied numerically in the Harper model. It is shown that interaction leads to appearance of localized states and pure-point spectrum component in the case…
Quasiperiodic systems serve as fertile ground for studying localisation, due to their propensity already in one dimension to exhibit rich phase diagrams with mobility edges. The deterministic and strongly-correlated nature of the…
Population structure can be modelled by evolutionary graphs, which can have a substantial, but very subtle influence on the fate of the arising mutants. Individuals are located on the nodes of these graphs, competing with each other to…
We investigate a simple generative model for network formation. The model is designed to describe the growth of networks of kinship, trading, corporate alliances, or autocatalytic chemical reactions, where feedback is an essential element…
In this paper we focus on spatial Markov population models, describing the stochastic evolution of populations of agents, explicitly modelling their spatial distribution, representing space as a discrete, finite graph. More specifically, we…
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of…
In the stochastic sandpile model on a graph, particles interact pairwise as follows: if two particles occupy the same vertex, they must each take an independent random walk step with some probability $0<p<1$ of not moving. These…
We consider a class of continuous-time stochastic growth models on $d$-dimensional lattice with non-negative real numbers as possible values per site. The class contains examples such as binary contact path process and potlatch process. We…
The link between a particular class of growth processes and random matrices was established in the now famous 1999 article of Baik, Deift, and Johansson on the length of the longest increasing subsequence of a random permutation. During the…
The emergence of collective dynamics in neural networks is a mechanism of the animal and human brain for information processing. In this paper, we develop a computational technique using distributed processing elements in a complex network,…