Related papers: Phase transitions in social sciences: two-populati…
Mutualistic interactions, where individuals from different species can benefit from each other, are widespread across ecosystems. This study develops a general deterministic model of mutualism involving two populations, assuming that…
A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…
We propose a thermodynamic multi-state spin model in order to describe equilibrial behavior of a society. Our model is inspired by the Axelrod model used in social network studies. In the framework of the statistical mechanics language, we…
Recently a computational model has been proposed of the social integration, as described in sociological terms by Peter Blau. In this model, actors praise or critique each other, and these actions influence their social status and raise…
In this paper we review some recent results dealing with the transition between microscopic and macroscopic scales in different fields, including kinetic theory, cells movement in biology, chemotaxis, flocking phenomena and agent systems.…
There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations -- within simple models, both are obtained from the principal eigenvector of the same…
This paper proposes a conditional Curie-Weiss model as a model for opinion formation in a society polarized along two opinions, say opinions 1 and 2. The model comes with interaction strength $\beta>0$ and bais $h$. Here the population in…
Increased day-trading activity and the subsequent jump in intraday volatility and trading volume fluctuations has raised considerable interest in models for financial market microstructure. We investigate the random transitions between two…
Mean-field approximation is often used to explore the qualitative behaviour of phase transitions in classical spin models before employing computationally costly methods such as the Monte-Carlo techniques. We implement a 'lattice…
We study the critical behavior of a general contagion model where nodes are either active (e.g. with opinion A, or functioning) or inactive (e.g. with opinion B, or damaged). The transitions between these two states are determined by (i)…
We study binary state contagion dynamics on a social network where nodes act in response to the average state of their neighborhood. We model the competing tendencies of imitation and non-conformity by incorporating an off-threshold into…
Heterogeneous adoption thresholds exist widely in social contagions, but were always neglected in previous studies. We first propose a non-Markovian spreading threshold model with general adoption threshold distribution. In order to…
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
We study phase transitions in models of opinion formation which are based on the social impact theory. Two different models are discussed: (i) a cellular--automata based model of a finite group with a strong leader where persons can change…
In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well…
The driven transport of plastic systems in various disordered backgrounds is studied within mean field theory. Plasticity is modeled using non-convex interparticle potentials that allow for phase slips. This theory most naturally describes…
We consider the Ising model for two interacting groups of spins embedded in an Erd\"{o}s-R\'{e}nyi random graph. The critical properties of the system are investigated by means of extensive Monte Carlo simulations. Our results evidence the…
We consider a system of hierarchical interacting spins under dynamics of spin-flip type with a ferromagnetic mean field interaction, scaling with the hierarchical distance, coupled with a system of linearly interacting hierarchical…
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the interacting boson model. A mean-field analysis links different regions of the parameter space with definite geometric shapes.…