Search and foraging : individual motion and swarm dynamics PDF
Preview Search and foraging : individual motion and swarm dynamics
Search 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 MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software. CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2015 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20150506 International Standard Book Number-13: 978-1-4822-4210-2 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid- ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. 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Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com © 2015 by Taylor & Francis Group, LLC 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 © 2015 by Taylor & Francis Group, LLC 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 © 2015 by Taylor & Francis Group, LLC 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
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