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Belief perseverance is the widely documented tendency of holding to a belief, even in the presence of contradicting evidence. In online environments, this tendency leads to heated arguments with users ``blocking'' each other. Introducing…
Deterministic dynamics is a mathematical model used to describe the temporal evolution of a system, generally expressed as dx/dt = F(x), where x represents the system's state, and F(x) determines its dynamics. It is employed to understand…
The spatial organization of individuals and their interactions in communities are important factors known to preserve diversity in many complex systems. Inspired by metapopulation models from ecology, we study opinion formation using a…
People's opinions on a wide range of topics often evolve over time through their interactions with others. Models of opinion dynamics primarily focus on one-dimensional opinions, which represent opinions on one topic. However, opinions on…
The complexity of human behaviour can lead to very unpredictable patterns in social activity and structure. Here we demonstrate the instability of a community network controlled by majority ruling, where an element adopts the most popular…
Distributed control increases system scalability, flexibility, and redundancy. Foundational to such decentralisation is consensus formation, by which decision-making and coordination are achieved. However, decentralised multi-agent systems…
Reputation-based cooperation on social networks offers a causal mechanism between graph properties and social trust. Recent papers on the `structural microfoundations` of the society used this insight to show how demographic processes, such…
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…
The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters they might share the benefit of cooperation while being more protected against non-cooperating individuals, which…
Online social networks have become primary means of communication. As they often exhibit undesirable effects such as hostility, polarisation or echo chambers, it is crucial to develop analytical tools that help us better understand them. In…
We present exact results for a lattice model of cluster growth in 1D. The growth mechanism involves interface hopping and pairwise annihilation supplemented by spontaneous creation of the stable-phase, +1, regions by overturning the…
Understanding how opinions spread through a community or how consensus emerges in noisy environments can have a significant impact on our comprehension of social relations among individuals. In this work a model for the dynamics of opinion…
We investigate a class of models for opinion dynamics in a population with two interacting families of individuals. Each family has an intrinsic mean field "Voter-like" dynamics which is influenced by interaction with the other family. The…
We study opinion dynamics on networks with a nontrivial community structure, assuming individuals can update their binary opinion as the result of the interactions with an external influence with strength $h\in [0,1]$ and with other…
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…
Inspired by the Deffuant and Hegselmann-Krause models of opinion dynamics, we extend the Kuramoto model to account for confidence bounds, i.e., vanishing interactions between pairs of oscillators when their phases differ by more than a…
People's opinions change with time as they interact with each other. In a bounded-confidence model (BCM) of opinion dynamics, individuals (which are represented by the nodes of a network) have continuous-valued opinions and are influenced…
Understanding the dynamics of opinion depolarization is pivotal to reducing the political divide in our society. We propose an opinion dynamics model, which we name the social compass model, for interdependent topics represented in a polar…
This paper gives lower bounds for the probability of consensus for two spatially explicit stochastic opinion models. Both processes are characterized by two finite connected graphs, that we call respectively the spatial graph and the…
The one-dimensional contact process is analyzed by a cluster approximation. In this approach, the hierarchy of rate equations for the densities of finite length empty intervals are truncated under the assumption that adjacent intervals are…