本书共8章，内容包括：第1章是引言，介绍本书的写作背景和基本情况。第2章对本书用到的基础知识进行介绍。第3章研究基本的带有随机噪声的Hegselmann-Krause模型的同步行为。第4章研究全状态空间下随机噪声引导系统同步的理论。第5章研究异质模型在环境噪声及通讯噪声作用下的演化。第6章应用前文理论研究社会舆论分歧产生的模型和机制。第7章介绍随机信息流产生真相的相关理论。第8章介绍利用随机噪声消除群体分歧的干预策略。
1 Introduction
1.1 Motivation and Background
1.2 Outline of the Book
References
2 Preliminaries
2.1 Basic Definitions
2.2 Main Theorems
References
3 Homogeneous HK Model in Bounded Space
3.1 HK Models
3.2 Critical Noise for Quasi-Consensus
3.3 Sufficient Condition for Quasi-Consensus
3.4 Necessary Condition for Quasi-Consensus
3.5 Simulations
3.6 Notes
References
4 Homogeneous HK Model in Unbounded Space
4.1 Model and Definitions
4.2 Main Results
4.3 Simulations
4.4 Notes
References
5 Heterogeneous HK Model with Environment and Communication Noise
5.1 Models and Definitions
5.1.1 Heterogeneous Mode]s with Environment Noise
5.1.2 Heterogeneous Models with Communication Noise
5.1.3 Definitions
5.2 Main Results for Quasi-Synchronization
5.2.1 Proofs of Theorems 5. l and 5.2, and Corollaries 5.1 and 5.2
5.2.2 Proofs of Theorems 5.3 and 5.4
5.3 Increasing Confidence Thresholds May Harm Synchronization under System (5.3)
5.4 Notes
References
6 Random Information Flow Benefits Truth Seeking
6.1 Preliminary and Formulation
6.1.1 Truth Seeking Model
6.1.2 Free Information Flow
6.1.3 Approach Truth
6.2 Main Results
6.3 Simulations
6.4 Notes
References
7 Elimination of Disagreement via Covert Noise
7.1 Preliminaries and Formulation
7.1.1 HK-Based Divisive System
7.1.2 Noise Intervened System
7.1.3 φ-Consensus
7.2 φ-Consensus of Noise-Intervened System
7.3 soft Control Strategy
7.4 Stopping Time of Reaching 0-Consensus
7.5 Simulations
7.6 Notes
References
8 Robust Fragmentation of HK-Type Dynamics
8.1 φ-Consensus of HK-Type Models
8.1.1 Noisy HK-Type Models
8.1.2 6-Consensus
8.1.3 Spontaneous φ-Consensus Caused by Noise
8.2 HK Model with Heterogenous Prejudices
8.3 Simulations
8.4 Notes
References
Appendix A Proofs
A.1 Proof of Lemma 5.2
A.2 Proof of Lemma 5.3
A.3 Proof of Lemma 5.4
A.4 Proof of Lemma 5.5
A.5 Proof of Lemma 5.8
A.6 Proof of Lemma 5.9
A.7 Proof of Lemma 5.10
A.8 Proof of Lemma 5.11
A.9 Proof of Lemma 5.12
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