scholarly journals A stabilization theorem for dynamics of continuous opinions

2005 ◽  
Vol 355 (1) ◽  
pp. 217-223 ◽  
Author(s):  
Jan Lorenz
Keyword(s):  
Stabilization Theorem ◽  
Continuous Opinions

scholarly journals On Minimum-B Stabilization of Electrostatic Drift Instabilities

1966 ◽  
Vol 21 (11) ◽  
pp. 1953-1959 ◽  
Author(s):  
R. Saison ◽  
H. K. Wimmel
Keyword(s):  
Dispersion Relation ◽  
Particle Distribution ◽  
Inhomogeneous Plasma ◽  
Distribution Functions ◽  
Loss Cone ◽  
First Order ◽  
Stabilization Theorem ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Limiting Case

A check is made of a stabilization theorem of ROSENBLUTH and KRALL (Phys. Fluids 8, 1004 [1965]) according to which an inhomogeneous plasma in a minimum-B field (β ≪ 1) should be stable with respect to electrostatic drift instabilities when the particle distribution functions satisfy a condition given by TAYLOR, i. e. when f0 = f(W, μ) and ∂f/∂W < 0 Although the dispersion relation of ROSENBLUTH and KRALL is confirmed to first order in the gyroradii and in ε ≡ d ln B/dx z the stabilization theorem is refuted, as also is the validity of the stability criterion used by ROSEN-BLUTH and KRALL, ⟨j·E⟩ ≧ 0 for all real ω. In the case ωpi ≫ | Ωi | equilibria are given which satisfy the condition of TAYLOR and are nevertheless unstable. For instability it is necessary to have a non-monotonic ν ⊥ distribution; the instabilities involved are thus loss-cone unstable drift waves. In the spatially homogeneous limiting case the instability persists as a pure loss cone instability with Re[ω] =0. A necessary and sufficient condition for stability is D (ω =∞, k,…) ≦ k2 for all k, the dispersion relation being written in the form D (ω, k, K,...) = k2+K2. In the case ωpi ≪ | Ωi | adherence to the condition given by TAYLOR guarantees stability.

Delay Independent Control of Bilateral Teleoperation Based on LMI

2011 ◽  
Vol 138-139 ◽  
pp. 498-503
Author(s):  
Rui Qi Wang ◽  
Ke Hua Li ◽  
Heng Li ◽  
Chang Jun Xia
Keyword(s):  
Control System ◽  
State Space ◽  
Dynamic Equation ◽  
Function Method ◽  
Experimental Results ◽  
Channel Structure ◽  
Bilateral Teleoperation ◽  
Bilateral Control ◽  
Error Dynamic ◽  
Stabilization Theorem

This paper presents a delay independent algorithm for bilateral control system which necessary uses for achieving in teleoperation. The system uses a state space expression to implement error dynamic equation with a tow channel structure. Then, several linearity matrix inequations (LMI) called stabilization theorem are constructed. Lyaponov function method is used to prove the stabilization theorem. Experimental results show that our approach is valid and has encouraging stabilization performance.

Mixing beliefs among interacting agents

2000 ◽  
Vol 03 (01n04) ◽  
pp. 87-98 ◽  
Author(s):  
Guillaume Deffuant ◽  
David Neau ◽  
Frederic Amblard ◽  
Gérard Weisbuch
Keyword(s):  
Opinion Dynamics ◽  
Interacting Agents ◽  
Continuous Opinions

We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions towards an average opinion, whereas low thresholds result in several opinion clusters: members of the same cluster share the same opinion but are no longer influenced by members of other clusters.

scholarly journals THE SZNAJD CONSENSUS MODEL WITH CONTINUOUS OPINIONS

2005 ◽  
Vol 16 (01) ◽  
pp. 17-24 ◽  
Author(s):  
SANTO FORTUNATO
Keyword(s):  
Real Number ◽  
Simple Extension ◽  
Consensus Model ◽  
Confidence Bound ◽  
Two Agents ◽  
Bounded Confidence ◽  
Consensus Models ◽  
The Mean ◽  
Continuous Opinions

In the consensus model of Sznajd, opinions are integers and a randomly chosen pair of neighboring agents with the same opinion forces all their neighbors to share that opinion. We propose a simple extension of the model to continuous opinions, based on the criterion of bounded confidence which is at the basis of other popular consensus models. Here, the opinion s is a real number between 0 and 1, and a parameter ∊ is introduced such that two agents are compatible if their opinions differ from each other by less than ∊. If two neighboring agents are compatible, they take the mean sm of their opinions and try to impose this value to their neighbors. We find that if all neighbors take the average opinion sm, the system reaches complete consensus for any value of the confidence bound ∊. We propose as well a weaker prescription for the dynamics and discuss the corresponding results.

scholarly journals CONTINUOUS OPINION DYNAMICS UNDER BOUNDED CONFIDENCE: A SURVEY

2007 ◽  
Vol 18 (12) ◽  
pp. 1819-1838 ◽  
Author(s):  
JAN LORENZ
Keyword(s):  
Social Psychology ◽  
Homogeneous Model ◽  
Opinion Dynamics ◽  
Complexity Science ◽  
Bifurcation Diagrams ◽  
Agent Based ◽  
Open Questions ◽  
Bounded Confidence ◽  
Cluster Configuration ◽  
Continuous Opinions

Models of continuous opinion dynamics under bounded confidence have been presented independently by Krause and Hegselmann and by Deffuant et al. in 2000. They have raised a fair amount of attention in the communities of social simulation, sociophysics and complexity science. The researchers working on it come from disciplines such as physics, mathematics, computer science, social psychology and philosophy. In these models agents hold continuous opinions which they can gradually adjust if they hear the opinions of others. The idea of bounded confidence is that agents only interact if they are close in opinion to each other. Usually, the models are analyzed with agent-based simulations in a Monte Carlo style, but they can also be reformulated on the agent's density in the opinion space in a master equation style. The contribution of this survey is fourfold. First, it will present the agent-based and density-based modeling frameworks including the cases of multidimensional opinions and heterogeneous bounds of confidence. Second, it will give the bifurcation diagrams of cluster configuration in the homogeneous model with uniformly distributed initial opinions. Third, it will review the several extensions and the evolving phenomena which have been studied so far, and fourth it will state some open questions.

Effects of selective attention on continuous opinions and discrete decisions

2010 ◽  
Vol 389 (18) ◽  
pp. 3711-3719 ◽  
Author(s):  
Xia-Meng Si ◽  
Yun Liu ◽  
Fei Xiong ◽  
Yan-Chao Zhang ◽  
Fei Ding ◽  
...  
Keyword(s):  
Selective Attention ◽  
Continuous Opinions

ADAPTIVE SLIDING-MODE CONTROL: SIMPLEX-TYPE METHOD

2015 ◽  
Vol 39 (3) ◽  
pp. 367-377
Author(s):  
Ta-Tau Chen
Keyword(s):  
Adaptive Control ◽  
Sliding Mode Control ◽  
Simplex Method ◽  
Sliding Mode ◽  
Adaptive Sliding Mode Control ◽  
Type Method ◽  
Adaptive Sliding Mode ◽  
Mode Control ◽  
Chattering Phenomenon ◽  
Stabilization Theorem

The simplex method is easy and brief for designing the sliding mode, but it also has some disadvantages. Since the control vectors are constant, the chattering phenomenon also occurs when switching control takes place in simplex-type SMC scheme. Hence, we make few modifications to the simplex method that form an irregular simplex such that it improves the choice of simplex control vector and chattering phenomenon. The irregular simplex is obtained by an adaptive control law. The stabilization of a nonlinear multi-input system by using adaptive control based on simplex-type sliding-mode control philosophy is examined in this paper. The adaptive law and stabilization theorem are proposed and proved. The simulation results demonstrate that the simplex-type adaptive sliding-mode control proposed in this paper is a good solution to the chattering problem in the simplex sliding-mode control.

scholarly journals Modeling and Simulation of Polarization in Internet Group Opinions Based on Cellular Automata

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Yaofeng Zhang ◽  
Renbin Xiao
Keyword(s):  
Cellular Automata ◽  
Modeling And Simulation ◽  
Opinion Leaders ◽  
Coupling Mechanism ◽  
Group Consensus ◽  
External Influences ◽  
Global Coupling ◽  
Simulation Results ◽  
Group 2 ◽  
Continuous Opinions

Hot events on Internet always attract many people who usually form one or several opinion camps through discussion. For the problem of polarization in Internet group opinions, we propose a new model based on Cellular Automata by considering neighbors, opinion leaders, and external influences. Simulation results show the following: (1) It is easy to form the polarization for both continuous opinions and discrete opinions when we only consider neighbors influence, and continuous opinions are more effective in speeding the polarization of group. (2) Coevolution mechanism takes more time to make the system stable, and the global coupling mechanism leads the system to consensus. (3) Opinion leaders play an important role in the development of consensus in Internet group opinions. However, both taking the opinion leaders as zealots and taking some randomly selected individuals as zealots are not conductive to the consensus. (4) Double opinion leaders with consistent opinions will accelerate the formation of group consensus, but the opposite opinions will lead to group polarization. (5) Only small external influences can change the evolutionary direction of Internet group opinions.

scholarly journals A Survey on Nonstrategic Models of Opinion Dynamics

Games ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 65
Author(s):  
Michel Grabisch ◽  
Agnieszka Rusinowska
Keyword(s):  
Threshold Model ◽  
Opinion Dynamics ◽  
Time Varying ◽  
Binary Variable ◽  
Rule Model ◽  
Bounded Confidence ◽  
Degroot Model ◽  
Voter Models ◽  
Time Varying Models ◽  
Continuous Opinions

The paper presents a survey on selected models of opinion dynamics. Both discrete (more precisely, binary) opinion models as well as continuous opinion models are discussed. We focus on frameworks that assume non-Bayesian updating of opinions. In the survey, a special attention is paid to modeling nonconformity (in particular, anticonformity) behavior. For the case of opinions represented by a binary variable, we recall the threshold model, the voter and q-voter models, the majority rule model, and the aggregation framework. For the case of continuous opinions, we present the DeGroot model and some of its variations, time-varying models, and bounded confidence models.

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