Table Of ContentSearch and Foraging
Individual Motion and Swarm Dynamics
© 2015 by Taylor & Francis Group, LLC
© 2015 by Taylor & Francis Group, LLC
Search and Foraging
Individual Motion and Swarm Dynamics
Eugene Kagan
Ariel University and the Weizmann Institute of Science
Israel
Irad Ben-Gal
Tel Aviv University
Israel
© 2015 by Taylor & Francis Group, LLC
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To our teachers.
© 2015 by Taylor & Francis Group, LLC
© 2015 by Taylor & Francis Group, LLC
Contents
Preface...............................................................................................................................................xi
List of Figures ..................................................................................................................................xv
List of Symbols ...............................................................................................................................xxi
Chapter 1 Introduction ..................................................................................................................1
1.1 Group Testing ....................................................................................................1
1.2 Search and Screening ........................................................................................2
1.3 Games of Search ................................................................................................3
1.4 Foraging .............................................................................................................3
1.5 Goal and Structure of This Book ......................................................................5
Chapter 2 Methods of Optimal Search and Screening .................................................................7
2.1 Location Probabilities and Search Density .......................................................7
2.2 Search for a Static Target...................................................................................9
2.2.1 Constrained Search ..............................................................................9
2.2.2 Group-Testing Search .........................................................................18
2.2.3 Sequential Search ...............................................................................21
2.2.4 Search by Areas..................................................................................22
2.3 Search for a Moving Target .............................................................................27
2.3.1 Basic Two-Cell Models ......................................................................27
2.3.2 Moving Target Search in Discrete Domain ........................................31
2.3.3 Moving Target Search in Continuous Domain ...................................40
2.4 Summary .........................................................................................................44
Chapter 3 Methods of Optimal Foraging ....................................................................................45
3.1 Preying and Foraging by Patches ....................................................................45
3.2 Spatial Dynamics of Populations ....................................................................47
3.3 Methods of Optimal Foraging .........................................................................51
3.3.1 General Assumptions and Deterministic Foraging ............................51
3.3.2 Foraging in Stochastic Environment ..................................................57
3.3.2.1 Oaten Model .......................................................................58
3.3.2.2 McNamara Model ...............................................................65
3.3.2.3 Foraging in Discrete Space and Time ................................68
3.3.3 Preying Model and Pursuit-Evasion Game ........................................71
3.4 Inferences and Restrictions .............................................................................74
3.5 Summary .........................................................................................................75
Chapter 4 Models of Individual Search and Foraging ................................................................77
4.1 Movements of the Agents and Their Trajectories ...........................................77
4.2 Brownian Search and Foraging .......................................................................79
4.2.1 Simple Brownian Search ....................................................................79
4.2.1.1 Random Walk in Discrete Domain.....................................79
4.2.1.2 Simple Brownian Motion ....................................................83
vii
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viii Contents
4.2.2 Correlated Brownian Motion and the Model of the Agent ................86
4.2.3 Fractional Brownian Motion ..............................................................92
4.3 Foraging by Lévy Flights ................................................................................98
4.3.1 Lévy Flights .......................................................................................98
4.3.2 Search and Foraging by Lévy Flights ..............................................105
4.3.3 Intermittent Strategies and Relation with Foraging by Patches .......117
4.4 Algorithms of Probabilistic Search and Foraging .........................................124
4.4.1 Search for Static and Moving Targets ..............................................124
4.4.2 Search for Static and Moving Targets: Errorless Detection .............125
4.4.3 Search for Static and Moving Targets: False-Negative Detection
Errors ................................................................................................131
4.4.4 Static Target Search in Noisy Environment: False-Positive and
False-Negative Detection Errors ......................................................134
4.4.5 Probabilistic Search with Shadowing ...............................................137
4.4.6 Remarks on Foraging with Obstacle Avoidance ..............................142
4.5 Summary .......................................................................................................143
Chapter 5 Coalitional Search and Swarm Dynamics ...............................................................145
5.1 Swarming and Collective Foraging ...............................................................145
5.2 Foraging by Multiple Foragers in Random Environment .............................148
5.2.1 Information Exchange and Usage of the Environment ....................148
5.2.1.1 Bio-signaling in the Search and Foraging Tasks ..............148
5.2.1.2 Stigmergy and Indirect Communication ..........................154
5.2.2 Algorithms of Foraging by Multiple Agents ....................................160
5.2.2.1 Search with Common Target’s Location Probabilities .....160
5.2.2.2 Foraging with Direct Communication Using
Bio-signaling .....................................................................163
5.2.2.3 Foraging with Indirect Communication ...........................167
5.2.3 Simulation Results of Group Foraging with Direct
Communication ..............................................................................171
5.3 Modeling by Active Brownian Motion ..........................................................176
5.3.1 Active Brownian Particles ................................................................176
5.3.1.1 Langevin Equation for Simple Brownian Motion ............177
5.3.1.2 Brownian Motion in External Potential Field ...................178
5.3.1.3 Active Brownian Motion ..................................................180
5.3.2 Multiagent Systems and Canonical Active Brownian Motion .........184
5.3.3 Distributions of Turning Angles for Active Brownian Agents ........191
5.4 Turing System for the Swarm Foraging ........................................................194
5.4.1 Turing System for the Target–Searcher Dynamics ..........................197
5.4.1.1 Remarks on the Dynamics of Turing System ...................197
5.4.1.2 Target–Searcher System ...................................................203
5.4.2 Ordering and Disordering Phenomena and Stability of the
Patterns .............................................................................................207
5.4.2.1 Self-Organization and Stability of Turing Patterns ..........207
5.4.2.2 Spatial and Temporal Patterns in Target–Searcher
System ...............................................................................210
5.4.3 Model of Social Foraging .................................................................212
5.5 Summary .......................................................................................................218
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Contents ix
Chapter 6 Remarks on Swarm Robotic Systems for Search and Foraging ...............................219
Chapter 7 Conclusion ................................................................................................................223
Bibliography ...................................................................................................................................225
Index ..............................................................................................................................................237
© 2015 by Taylor & Francis Group, LLC
© 2015 by Taylor & Francis Group, LLC
