Related papers: Time-delay Induced Dimensional Crossover in Voter …
We investigate the effects of delayed interactions on the stationary distribution of the noisy voter model. We assume that the delayed interactions occur through the periodic polling mechanism and replace the original instantaneous…
We study analytically the ordering kinetics of the two-dimensional long-range voter model on a two-dimensional lattice, where agents on each vertex take the opinion of others at distance $r$ with probability $P(r) \propto r^{-\al}$. The…
We study the ordering kinetics of a generalization of the voter model with long-range interactions, the $p$-voter model, in one dimension. It is defined in terms of boolean variables $S_{i}$, agents or spins, located on sites $i$ of a…
We analyze the scaled voter model, which is a generalization of the noisy voter model with time-dependent herding behavior. We consider the case when the intensity of herding behavior grows as a power-law function of time. In this case, the…
In this work, we investigate interactions that simultaneously order a system locally, while keeping it globally disordered. The study is done in the context of the emergence of diversity in opinion propagation models with interactions…
The one-dimensional long-range voter model, where an agent takes the opinion of another at distance $r$ with probability $\propto r^{-\alpha}$, is studied analytically. The model displays rich and diverse features as $\alpha$ is changed.…
We study the bidimensional voter model on a square lattice with numerical simulations. We demonstrate that the evolution takes place in two distinct dynamic regimes; a first approach towards critical site percolation and a further approach…
Recent experiments in adult mammalian tissues have found scaling relations of the voter model in the dynamics of the genetically labeled population of stem cells. Yet, the reason for this seemingly robust appearance of the voter model…
We consider a lattice model in which a tracer particle moves in the presence of randomly distributed immobile obstacles. The crowding effect due to the obstacles interplays with the quasi-confinement imposed by wrapping the lattice onto a…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
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 the appearance of first-order dynamical phase transitions (DPTs) as `intermittent' co-existing phases in the fluctuations of random walks on graphs. We show that the diverging time scale leading to critical behaviour is the waiting…
A voting model (or a generalization of the Glauber model at zero temperature) on a multidimensional lattice is defined as a system composed of a lattice each site of which is either empty or occupied by a single particle. The reactions of…
In this paper we investigate the scaling limit of the range (the set of visited vertices) for a class of critical lattice models, starting from a single initial particle at the origin. We give conditions on the random sets and an associated…
Consider the voter model on a box of side length $L$ (in the triangular lattice) with boundary votes fixed forever as type 0 or type 1 on two different halves of the boundary. Motivated by analogous questions in percolation, we study…
In the Schr\"odinger evolution of a quantum state time enters as a real parameter representing the coordinate. In a more consistent approach time should be defined as a quantum observable, with the evolution taking place in a…
The exploration of dimensional crossover carries profound fundamental significance, serving as a crucial bridge in comprehending the remarkable disparities observed in transitional phenomena across the two distinct dimensions of a physical…
The voter model is a classical interacting particle system, modelling how global consensus is formed by local imitation. We analyse the time to consensus for a particular family of voter models when the underlying structure is a scale-free…
High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems…
We consider the patterns of collective motion emerging when many aligning, self-propelling units move in two dimensions while interacting through a repulsive potential and are also subject to delays and random perturbations. In this…