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The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. In this paper, we derive a Fractional Fokker--Planck equation for the probability distribution of…
Diffusion theory establishes a fundamental connection between stochastic differential equations and partial differential equations. The solution of a partial differential equation known as the Fokker-Planck equation describes the…
Understanding the evolution of collective beliefs is of critical importance to get insights on the political trends as well as on social tastes and opinions. In particular, it is pivotal to develop analytical models that can predict the…
Spatial pattern formation in excitable fluctuating media was researched analytically from the point of view of the order parameters concept. The reaction-diffusion system in external noise is considered as a model of such medium. Stochastic…
The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. However, there are both theoretical and empirical reasons to consider similar equations driven by…
We analyse the non-equilibrium distribution in dissipative dynamical systems at finite noise intensities. The effect of finite noise is described in terms of topological changes in the pattern of optimal paths. Theoretical predictions are…
Memory effects play a crucial role in social interactions and decision-making processes. This paper proposes a novel fractional-order bounded confidence opinion dynamics model to characterize the memory effects in system states. Building…
We consider the mean field Fokker-Planck equation subject to nonlinear no-flux boundary conditions, which necessarily arise when subjecting a system of Brownian particles interacting via a pair potential in a bounded domain. With the…
Bounded confidence opinion dynamics model the propagation of information in social networks. However in the existing literature, opinions are only viewed as abstract quantities without semantics rather than as part of a decision-making…
Score-based generative models (SGMs) learn a family of noise-conditional score functions corresponding to the data density perturbed with increasingly large amounts of noise. These perturbed data densities are linked together by the…
The influence of crowding on the diffusion of tagged particles in a dense medium is investigated in the framework of a mean-field model, derived in the continuum limit from a microscopic stochastic process with exclusion. The probability…
The majority-vote model with noise is one of the simplest nonequilibrium statistical model that has been extensively studied in the context of complex networks. However, the relationship between the critical noise where the order-disorder…
We analyze a simple opinion formation model consisting of two parties, A and B, and a group I, of undecided agents. We assume that the supporters of parties A and B do not interact among them, but only interact through the group I, and that…
Motivated by the dynamics of cultural change and diversity, we generalize the three-species constrained voter model on a complete graph introduced in [J. Phys. A 37, 8479 (2004)]. In this opinion dynamics model, a population of size N is…
In this era of fast and large-scale opinion formation, a mathematical understanding of opinion evolution, a.k.a. opinion dynamics, is especially important. Linear graph-based dynamics and bounded confidence dynamics are the two most popular…
We propose a new approach to describe the effective microscopic dynamics of (power-law) nonlinear Fokker-Planck equations. Our formalism is based on a nonextensive generalization of the Wiener process. This allow us to obtain, in addition…
We study the evolution of opinions on a directed network with community structure. Individuals update their opinions synchronously based on a weighted average of their neighbors' opinions, their own previous opinions, and external media…
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…
Opinion dynamics, the study of how individual beliefs and collective public opinion evolve, is a fertile domain for applying statistical physics to complex social phenomena. Like physical systems, societies exhibit macroscopic regularities…
The modeling of opinion dynamics has seen much study in varying academic disciplines. Understanding the complex ways information can be disseminated is a complicated problem for mathematicians as well as social scientists. We present a…