Consensus formation of two-level opinion dynamics

Opinion dynamics have received significant attention in recent years. This paper proposes a bounded confidence opinion model for a group of agents with two different confidence levels. Each agent in the population is endowed with a confidence interval around her opinion with radius αd or (1-α)d, where α ∈ (0,1/2] represents the differentiation of confidence levels. We analytically derived the critical confidence bound d_c = 1/(4α) for the two-level opinion dynamics on ?. A single opinion cluster is formed with probability 1 above this critical value regardless of the ratio p of agents with high/low confidence. Extensive numerical simulations are performed to illustrate our theoretical results. Noticed is a clear impact of p on the collective behavior: more agents with high confidence lead to harder agreement. It is also experimentally revealed that the sharpness of the threshold d_c increases with α but does not depend on p.     

Dissonance Minimization as a Microfoundation of Social Influence in Models of Opinion Formation

Models of opinion formation are used to investigate many collective phenomena. While social influence often constitutes a basic mechanism, its implementation differs between the models. In this article, we provide a general framework of social influence based on dissonance minimization. We only premise that individuals strive to minimize dissonance resulting from different opinions compared to individuals in a given social network. Within a game theoretic context, we show that our concept of dissonance minimization resembles a coordination process when interactions are homogeneous. We further show that different models of opinion formation can be represented as best response dynamics within our framework. Thus, we offer a unifying perspective on these heterogeneous models and link them to rational choice theory.     

Voter models and external influence

ABSTRACT

In this paper, we extend the voter model (VM) and the threshold voter model (TVM) to include external influences modeled as a jump process. We study the newly-formulated models both analytically and computationally, employing diffusion approximations and mean field approximations. We derive results pertaining to the probability of reaching consensus on a particular opinion and also the expected consensus time. We find that although including an external influence leads to a faster consensus in general, this effect is more pronounced in the VM as compared to the TVM. Our findings suggest the potential importance of external influences in addition to local interactions.     

Krause's model of opinion dynamics on isolated time scales

We analyze a bounded confidence model, introduced by Krause, on isolated time scales. In this model, each agent takes into account only the assessments of the agents whose opinions are not too far away from its own opinion. We show that the behavior of the model depends strongly on the graininess function μ: If μ takes values in the interval ]0,1], then our discrete time scale model behaves similarly to the classical one, but if μ takes values in ]1,+∞[, then the model has different properties. Simulations are performed to validate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

基于社会网络的舆情传播模型构建与分析

本文考虑个体间的相互作用,提出了一个基于社会网络分析的舆情传播模型.模型假设网络中每个个体的初始状态只有两种情况,并且在单位时间步内只选择一个邻居进行交流,并以概率λ接受该邻居的意见.解析结果显示存在概率λc使得网络中持某种观点人数比例的期望值是一个常数,而其它状态下系统中所有个体的意见都会达成一致.本模型有助于衡量某给定社会网络中舆论传播的快慢程度.     

Evolutionary dynamics of the spatial Prisoner’s Dilemma with self-inhibition

In this paper we study the influence of interventions on self-interactions in a spatial Prisoner’s Dilemma on a two-dimensional grid with periodic boundary conditions and synchronous updating of the dynamics. We investigate two different types of self-interaction modifications. The first type (FSIP) is deterministic, effecting each self-interaction of a player by a constant factor, whereas the second type (PSIP) performs a probabilistic interventions. Both types of interventions lead to a reduction of the payoff of the players and, hence, represent inhibiting effects. We find that a constant but moderate reduction of self-interactions has a very beneficial effect on the evolution of cooperators in the population, whereas probabilistic interventions on self-interactions are in general counter productive for the coexistence of the two different strategies.     

A numerical method for the dynamics and stability of spiral waves

In this paper we propose a new method of investigating the change of dynamics in reaction-diffusion equations, which is based on approximating the Euclidian norm of state variables along with the introduction of phase space. Our method is simple in implementation and can be applied to study the dynamics of multiple spirals. The method is extended to study the stability of spiral waves by developing an algorithm which is applied to circular and meandering motions.     

Mixing of the Glauber dynamics for the ferromagnetic Potts model

We present several results on the mixing time of the Glauber dynamics for sampling from the Gibbs distribution in the ferromagnetic Potts model. At a fixed temperature and interaction strength, we study the interplay between the maximum degree (Δ) of the underlying graph and the number of colours or spins (q) in determining whether the dynamics mixes rapidly or not. We find a lower bound L on the number of colours such that Glauber dynamics is rapidly mixing if at least L colours are used. We give a closely‐matching upper bound U on the number of colours such that with probability that tends to 1, the Glauber dynamics mixes slowly on random Δ‐regular graphs when at most U colours are used. We show that our bounds can be improved if we restrict attention to certain types of graphs of maximum degree Δ, e.g. toroidal grids for Δ = 4. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 48, 21–52, 2016     

A new model family for the strength distribution of fibers in relation to their length

Based on the weakest-link model, a family of fiber strength distributions is investigated assuming a two-stage failure process. At the first stage, a weakest link is formed (instantly or gradually), but at the second one the fracture of this link takes place. The gradual accumulation of flaws is described with the aid of Markov chain theory. The adequacy of the models considered is verified by checking them against experimental strength data for E-glass and flax fibers of various lengths. It is found that the models are not less accurate, but are even better, in a number of cases, than the model based on the known modified Weibull model with a power-law relation between the fiber length and the scale parameter. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 179–192, March–April, 2006.     

Analysis of the fiber length dependence of its strength by using the weakest-link approach 2. Analysis of test data

A method for estimating the model parameters is described, the results found in processing glass, flax, and carbon fiber and carbon bundle datasets are reported, and a comparison of different models is given. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 65–74, January–February, 2008.     

Analysis of the fiber length dependence of its strength by using the weakest-link approach 1. A family of weakest-link distribution functions

This paper presents a summary and further development of the ideas proposed in the previous papers of the authors, which were dedicated to investigating the fiber scale effect (strength-length relation). In the first part of the paper, some theoretical aspects of the problem are considered; in the second one, an application to the processing of test datasets is discussed. As distinct from our previous publications, two types of defects (“technological,” i.e., existing before loading, and load-dependent) and two types of influence of the number of defects on the fiber strength are considered; the probability of absence of defects is also taken into account. We consider a specimen as a sequence of n elements of the same length. It is supposed that there are defects in K of them, 0 ≤ K ≤ n. Two cases are considered: K is a random variable or a random process K (t). In the second case, the increase in K and the failure of a specimen is described as a Markov chain whose matrix of transition probabilities depends on the current value of the loading process, described as some (increasing to infinity) sequence {x₁, x₂, …, x_t,…}. Three versions of relationships between the specimen strength and the number of defective elements are considered for both the cases. Thus, six probability structures are introduced, and different versions of distribution functions and the corresponding models are considered. The methods for estimating the model parameters, the results obtained in processing glass, flax, carbon fiber, and carbon bundle datasets, as well as a comparison of different models, are presented in the second part of the paper. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 5, pp. 685–696, September–October, 2008.     

Global stability of the virus dynamics model with intracellular delay and Crowley–Martin functional response

In this paper, a virus dynamics model with intracellular delay and Crowley–Martin functional response is discussed. By constructing suitable Lyapunov functions and using LaSalles invariance principle for delay differential equations, we established the global stability of uninfected equilibrium and infected equilibrium; it is proved that if the basic reproductive number is less than or equal to one, the uninfected equilibrium is globally asymptotically stable; if the basic reproductive number is more than one, the infected equilibrium is globally asymptotically stable. We also discuss the effects of intracellular delay on global dynamical properties by comparing the results with the stability conditions for the model without delay. Copyright © 2013 John Wiley & Sons, Ltd.     

A fibre microbuckling model for predicting the notched compressive strength of composite sandwich panels

Cohesive-zone models have been successfully applied to predicting the damage from notches in engineering materials loaded intension. They have also been used to determine the growth of fibre microbuckling from a hole in a composite laminate under compression. The usual strategy is to replace the in elastic deformation associated with plasticity or microbuckling with a line crack and to assume some form of stress-displacement bridging law across the crack faces. This paper examines recent published experimental data for notched glass-fibre epoxy/honey comb sand wich panels loaded in uniaxial compression. A plastic fibre kinking analysis and a linear softening cohesive-zone model are used for the prediction of the unnotched and open-hole compressive strength and the theoretical results are found to be in a good agreement with experimental data. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 73–84, January–February, 2007.     

Positive computational modelling of the dynamics of active and inert biomass with extracellular polymeric substances

Departing from a complex system of nonlinear partial differential equations that models the growth dynamics of biological films, we provide a finite-difference model to approximate its solutions. The variables of interest are measured in absolute scales, whence the need of preserving the positivity of the solutions is a mathematical constraint that must be observed. In this work, we provide a numerical discretization of our mathematical model which is capable of preserving the non-negative character of approximations under suitable conditions on the model and computational parameters. As opposed to the nonlinear model which motivates this report, our numerical technique is a linear method which, under suitable circumstances, may be represented by an M-matrix. The fact that our method is a positivity-preserving scheme is established using the inverse-positive properties of these matrices. Computer simulations corroborate the validity of the theoretical findings.