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
鄂公網(wǎng)安備 42010302001612號(hào) 