Related papers: Stability Theory of Stochastic Models in Opinion D…
The dynamics of opinion formation in large groups of people is a complex non-linear phenomenon whose investigation is just at the beginning. Both collective behaviour and personal view play an important role in this mechanism. In the…
In traditional voter models, opinion dynamics are driven by interactions between individuals, where an individual adopts the opinion of a randomly chosen neighbor. However, these models often fail to capture the emergence of entirely new…
We study pattern formation in the bounded confidence model of opinion dynamics. In this random process, opinion is quantified by a single variable. Two agents may interact and reach a fair compromise, but only if their difference of opinion…
Social interactions influence people's opinions. In some situations, these interactions eventually yield a consensus opinion; in others, they can lead to opinion fragmentation and the formation of different opinion groups in the form of…
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the…
We study a model for opinion formation which incorporates three basic ingredients for the evolution of the opinion held by an individual: imitation, influence of fashion and randomness. We show that in the absence of fashion, the model…
We introduce a stochastic model of binary opinion dynamics in one dimension. The binary opinions $\pm 1$ are analogous to up and down Ising spins and in the equivalent spin system, only the spins at the domain boundary can flip. The…
We study a model for social influence in which the agents' opinion is a continuous variable [G. Weisbuch et al., Complexity \textbf{7}, 2, 55 (2002)]. The convergent opinion adjustment process takes place as a result of random binary…
Motivated by stochastic models of climate phenomena, the steady-state of a linear stochastic model with additive Gaussian white noise is studied. Fluctuation theorems for nonequilibrium steady-states provide a constraint on the character of…
We consider the adaptive control problem for discrete-time, nonlinear stochastic systems with linearly parameterised uncertainty. Assuming access to a parameterised family of controllers that can stabilise the system in a bounded set within…
The dynamical origin of opinion polarization in the real world is an interesting topic physical scientists may help to understand. To properly model the dynamics, the theory must be fully compatible with findings by social psychologists on…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
We investigate majority-vote opinion dynamics on Geometric Inhomogeneous Random Graphs (GIRGs), a powerful model for spatial complex networks. In contrast to classic coarsening dynamics where a single opinion typically achieves global…
We present a dynamical theory of opinion formation that takes explicitly into account the structure of the social network in which in- dividuals are embedded. The theory predicts the evolution of a set of opinions through the social network…
The equilibrium distributions of a Markovian model describing the interaction of several classes of permanent connections in a network are analyzed. It has been introduced by Graham and Robert. For this model each of the connections has a…
In this paper we consider the modeling of opinion dynamics over time dependent large scale networks. A kinetic description of the agents' distribution over the evolving network is considered which combines an opinion update based on binary…
We develop a model for credit rating migration that accounts for the impact of economic state fluctuations on default probabilities. The joint process for the economic state and the rating is modelled as a time-homogeneous Markov chain.…
Opinion formation in the population has attracted extensive research interest. Various models have been introduced and studied, including the ones with individuals' free will allowing them to change their opinions. Such models, however,…
Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the…
From the perspective of probability, the stability of growing network is studied in the present paper. Using the DMS model as an example, we establish a relation between the growing network and Markov process. Based on the concept and…