Design and Control of Swarm Dynamics (eBook)

Preface 7
Acknowledgments 8
Contents 9
1 Complexity and Swarming Systems 12
2 A Biologically Inspired Approach to Collective Behaviors 15
2.1 Collective Animal Behaviors 15
2.2 Ethology 16
2.3 Why Biological Inspiration? 17
2.4 What Nature Teaches Us About Swarming 18
2.4.1 Self-Organization and the Importance of Order in Life 19
2.4.2 Positive Feedback and the Emergence of Order 21
2.4.3 Collective Behavior Without Large-Scale Order 22
2.4.4 Information Processing and Swarm Intelligence 23
References 24
3 A Physical Approach to Swarming 26
3.1 Self-Organization in Physicochemical Systems 26
3.1.1 Elementary Cellular Automata 27
3.1.2 Collective Phenomena in Physical Systems 29
3.1.3 Collective Motion 31
3.2 The Self-Propelled Particles (SPP) Model 33
3.2.1 Dynamical Foundations 33
3.2.2 Neighborhood of Interactions 35
3.2.3 Dynamic Update Rule 37
3.3 What Statistical Physics Teaches Us 38
3.3.1 Phase Transitions 39
3.3.2 Scaling and Universality 41
3.3.3 Fluctuations, Correlations, Susceptibility, and Nonapparent Collective Behavior 42
3.3.4 Nonequilibrium Systems and Self-Organized Criticality 45
3.4 What the Theory of Dynamical Systems Teaches Us 45
3.4.1 Bifurcation, Catastrophe, Collapse, and Tipping Point 46
3.4.2 At the Edge of Chaos 48
3.5 Inspiration and Swarm Design 49
References 50
4 A Network-Theoretic Approach to Collective Dynamics 53
4.1 A Science of Networks 53
4.2 Swarm Signaling Networks 55
4.3 Network Properties and Swarm Dynamics 57
4.3.1 Assembling the Swarm Signaling Network 57
4.3.2 Connectedness of the Signaling Network 59
4.3.3 Shortest Connecting Path 62
4.3.4 Clustering Coefficient 63
4.3.5 Degree Distribution 64
4.3.6 Resilience of Swarming 67
4.3.7 Controllability of Swarming 68
4.3.8 Swarm Network Dynamics 70
4.4 Design of Signaling Network for Artificial Swarming 71
4.4.1 Models of Signaling Networks 72
4.4.2 Enhanced Swarming Behaviors 76
4.4.3 Some Words of Caution 79
References 80
5 An Information-Theoretic Approach to Collective Behaviors 83
5.1 Social Information Transmission 83
5.2 Role of Information in Collective Behaviors 84
5.3 Information Flow in Swarms 85
5.3.1 Quantifying Information 85
5.3.2 Dynamics of Information Transfer 86
5.3.3 Transmission Channels 87
5.3.4 Capacity of the Transmission Channel 89
5.3.5 Informational Bottlenecks in Collective Behaviors 90
5.3.6 Conditions for the Emergence of Collective Behavior Under Data Rate Limitations 91
5.3.7 Swarming Collapse Under Data Rate Limitations 94
5.4 Information and Swarm Design 96
5.4.1 Acquisition of Stimuli Information by the Swarm 96
5.4.2 Dynamic Balancing of Positive and Negative Feedback Loops 97
5.4.3 Leveraging Technological Advances for Novel Swarm Designs 98
5.4.4 Coupling Between Information Flow and Agent's Movement 99
References 99
6 A Computational Approach to Collective Behaviors 102
6.1 From Collective Behavior to Computation and Information Processing 102
6.1.1 Nature of Information and Its Storage in Swarms 103
6.1.2 Swarms and Algorithms 104
6.2 The Theory of Computation 105
6.2.1 A Definition of Computation 105
6.2.2 The Concept of Computability 105
6.2.3 Computation and Causal Systems 106
6.2.4 Randomized Algorithms, Probabilistic Turing Machines, and Computation 107
6.3 Collective Information Processing in Swarms 107
6.3.1 A Tentative Classification of Collective Decision-Making Processes 108
6.3.2 The Importance of Randomness for Collective Computation 109
6.4 Computation and Swarm Design 110
References 111
7 Outlook: Can Swarms Be Designed? 112
References 113