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We construct an extension of the Lambda-coalescent to a spatial continuum and analyse its behaviour. Like the Lambda-coalescent, the individuals in our model can be separated into (i) a dust component and (ii) large blocks of coalesced…
The static and dynamic properties of a Cosserat-type lattice interface of finite thickness are studied, so that both displacements and rotational degrees of freedom are taken into account. The model allows considering interfaces with a…
A general model for opinion formation and competition, like in ideological struggles is formulated. The underlying set is a closed one, like a country but in which the population size is variable in time. Several ideologies compete to…
The Hotelling-Downs model considers parties changing policy to maximise their vote-share. Where policy position lies on a left-right axis, it describes a tendency for political parties to move towards centrist platforms. This is in contrast…
In this article, we study the effect of vector-valued interventions in votes under a binary voter model, where each voter expresses their vote as a $0-1$ valued random variable to choose between two candidates. We assume that the outcome is…
A boundary one point function related to the boundary spontaneous polarization, which is different from the ones considered in the past, is studied for the six vertex model on a 2N \times N lattice with domain wall boundary condition and…
We use Monte Carlo simulations and finite-size scaling theory to investigate the phase transition and critical behavior of the $S$-state block voter model on square lattices. It is shown that the system exhibits an order-disorder phase…
It is well-known that in two dimensions Turing systems produce spots, stripes and labyrinthine patterns, and in three dimensions lamellar and spherical structures or their combinations are observed. We study transitions between these states…
A model describing the three-dimensional folding of the triangular lattice on the face-centered cubic lattice is generalized allowing the presence of defects corresponding to cuts in the two-dimensional network. The model can be expressed…
Recent generalization of the coevolving voter model (J. Toruniewska et al, PRE 96 (2017) 042306) is further generalized here, including spin-dependent probability of rewiring. Mean field results indicate that either the system splits into…
This article starts by introducing a new theoretical framework to model spatial systems which is obtained from the framework of interacting particle systems by replacing the traditional graphical structure that defines the network of…
In this paper we study nonlinear $q$-voter model with stochastic driving on a complete graph. We investigate two types of stochasticity that, using the language of social sciences, can be interpreted as different kinds of nonconformity.…
For the voter model, we study the effect of a memory-dependent transition rate. We assume that the transition of a spin into the opposite state decreases with the time it has been in its current state. Counter-intuitively, we find that the…
The Langevin description of systems with two symmetric absorbing states yields a phase diagram with three different phases (disordered and active, ordered and active, absorbing) separated by critical lines belonging to three different…
We model an electorate voting on the funding of a public good in a two-party system in an evolutionary game theory framework. Voters adopt one of four strategies: Consensus-makers, Gridlockers, Party 1 Zealots, and Party 2 Zealots, which…
We investigate mean-field dynamics of a nonlinear opinion formation model with congregator and contrarian agents. Each agent assumes one of the two possible states. Congregators imitate the state of other agents with a rate that increases…
We investigate the dynamics of classical spins mapped as walkers in a virtual "spin" space using a generalised two-parameter family of spin models characterized by parameters $y$ and $z$ [M. J. de Oliveira, J. F. F. Mendes and M. A. Santos,…
We study positional voting rules when candidates and voters are embedded in a common metric space, and cardinal preferences are naturally given by distances in the metric space. In a positional voting rule, each candidate receives a score…
We study a model for the collective behavior of self-propelled particles subject to pairwise copying interactions and noise. Particles move at a constant speed $v$ on a two--dimensional space and, in a single step of the dynamics, each…
We study a process termed "agglomerative percolation" (AP) in two dimensions. Instead of adding sites or bonds at random, in AP randomly chosen clusters are linked to all their neighbors. As a result the growth process involves a diverging…