Frank Schweitzer

Brownian Agents and Active Particles.
Collective Dynamics in the Natural and Social Sciences

With a Foreword by J. Doyne Farmer

Berlin: Springer 2003 (Springer Series in Synergetics)
XVI, 420 p. 192 illus. Hardcover, ISBN 3-540-43938-2
EUR 59.95

"This book lays out a vision for a coherent framework for understanding complex systems'' (from the foreword by J. Doyne Farmer). By developing the genuine idea of Brownian agents, the author combines concepts from informatics, such as multiagent systems, with approaches of statistical many-particle physics. This way, an efficient method for computer simulations of complex systems is developed which is also accessible to analytical investigations and quantitative predictions. The book demonstrates that Brownian agent models can be successfully applied in many different contexts, ranging from physicochemical pattern formation, to active motion and swarming in biological systems, to self-assembling of networks, evolutionary optimization, urban growth, economic agglomeration and even social systems.

Keywords: Agent Models, Biological Systems, Brownian Agents, Complex Systems, Economic Agglomeration, Networks, Social Systems, Trail Formation

Table of Contents (Download pdf)


Foreword by J. Doyne Farmer

1.Complex Systems and Agent Models1
1.1Introduction to Agent-Based Modeling1
1.1.1The Micro-Macro Link1
1.1.2The Role of Computer Simulations3
1.1.3Agents and Multi-Agent Systems6
1.1.4Complex versus minimalistic agents10
1.1.5Agent Ecology13
1.1.6Simulation Approaches17
1.2Brownian Agents22
1.2.1Outline of the Concept22
1.2.2Interaction as Communication28
1.2.3A short survey of the book32
1.3Brownian Motion39
1.3.2Langevin Equation of Brownian Motion42
1.3.3Probability Density and Fokker-Planck Equation46
2.Active Particles51
2.1Active Motion and Energy Consumption51
2.1.1Storage of Energy in an Internal Depot51
2.1.2Velocity-Dependent Friction54
2.1.3Active Motion of Cells56
2.1.4Pumping By Space-Dependent Friction60
2.2Active Motion in One-Dimensional Systems65
2.2.1Adiabatic Approximations and Stationary Solutions65
2.2.2Stationary Velocities and Critical Parameters for U=const.67
2.2.3Stationary Solutions for a linear Potential U=ax70
2.2.4Deterministic Motion in a Ratchet Potential75
2.2.5Investigation of the Net Current82
2.2.6Stochastic Influences on the Net Current86
2.2.7Directed Motion in a Ratchet Potential92
2.3Active Motion in Two-Dimensional Systems95
2.3.1Distribution Function for U=const.95
2.3.2Deterministic Motion in a Parabolic Potential101
2.3.3Analytical Solutions for Deterministic Limit Cycle Motion103
2.3.4Deterministic Chaotic Motion in the Presence of Obstacles108
2.3.5Stochastic Motion in a Parabolic Potential109
2.3.6Stochastic Motion with Localized Energy Sources111
2.4Swarming of Active Particles114
2.4.1Canonical-Dissipative Dynamics of Swarms114
2.4.2Harmonic Swarms119
2.4.3Coupling via Mean Momentum and Mean Angular Momentum126
3.Aggregation and Physico-Chemical Structure Formation133
3.1Indirect Agent Interaction133
3.1.1Response to External Stimulation133
3.1.2Generation of the Effective Potential Field136
3.1.3Master Equations and Density Equations138
3.1.4Stochastic Simulation Technique141
3.2Aggregation of Brownian Agents145
3.2.1Chemotactic Response145
3.2.2Stability Analysis for Homogeneous Distributions146
3.2.3Estimation of an Effective Diffusion Coefficient151
3.2.4Competition of Spikes153
3.2.5Derivation of a Selection Equation156
3.2.6Comparison to Biological Aggregation159
3.3Pattern Formation in Reaction-Diffusion Systems164
3.3.1Coexistence of Spikes164
3.3.2Spiral Waves and Travelling Spots169
3.3.3Travelling Waves171
4.Self-Organization of Networks175
4.1Agent-Based Model of Network Formation175
4.1.1Basic Assumptions and Equations of Motion175
4.1.2Results of Computer Simulations179
4.2Estimation of the Network Connectivity182
4.2.1Critical Temperature182
4.2.2Network Connectivity and Threshold186
4.2.3Numerical Results190
4.3Construction of a Dynamic Switch192
4.3.1Setup for the Switch192
4.3.2Simulations of the Dynamic Switch194
4.3.3Estimation of the Switch Delay198
5.Tracks and Trail Formation in Biological Systems203
5.1Active Walker Models203
5.1.1Master Equation Approach to Active Walkers203
5.1.2Active Walker Models of Fractal Growth Patterns206
5.1.3Active Walker Models of Bacterial Growth208
5.2Discrete Model of Track Formation212
5.2.1Biased Random Walks212
5.2.2Reinforced Biased Random Walks217
5.2.3Formation of Tracks221
5.3Track Formation and Aggregation in Myxo-bacteria225
5.3.1Modification of the Active Walker Model225
5.3.2Simulation of Myxobacteria Aggregation228
5.4Trunk Trail Formation of Ants232
5.4.1Biological Observations232
5.4.2Active Walker Model of Trail Formation in Ants235
5.4.3Simulation of Trunk Trail Formation in Ants240
6.Movement and Trail Formation of Pedestrians247
6.1Movement of Pedestrians247
6.1.1The Social Force Model247
6.1.2Simulation of Pedestrian Motion249
6.2Trail Formation of Pedestrians251
6.2.1Model of Trail Formation251
6.2.2Human Trail Formation255
6.2.3Simulation of Pedestrian Trail Systems258
6.2.4Macroscopic Equations of Trail Formation261
7.Evolutionary Optimization Using Brownian Searchers267
7.1Evolutionary Optimization Strategies267
7.1.1Ensemble Search with Brownian Agents267
7.1.2Boltzmann Strategy and Darwin Strategy270
7.1.3Mixed Boltzmann--Darwin Strategy275
7.2Evaluation and Optimization of Road Networks279
7.2.1Road Networks279
7.2.2The Evaluation Function281
7.2.3Results of Computer Simulations284
7.3Asymptotic Results on the Optimization Landscape289
7.3.1Optimization Values in the Asymptotic Limit289
7.3.2Density of States in the Asymptotic Limit291
8.Analysis and Simulation of Urban Aggregation295
8.1Spatial Structure of Urban Aggregates295
8.1.1Urban Growth and Population Distribution295
8.1.2Mass Distribution of Urban Aggregates: Berlin300
8.1.3Fractal Properties of Urban Aggregates304
8.2Rank-Size Distribution of Urban Aggregates307
8.2.1Analysis of the Rank-Size Distribution307
8.2.2Master Equation Approach to Urban Growth309
8.2.3Simulation of the Rank-Size Distribution: Berlin312
8.2.4Forecast of the Future Evolution: Daegu315
8.3Kinetic Models of Urban Growth318
8.3.1Fractal Growth and Correlated Growth Models318
8.3.2Shift of Growth Zones322
8.3.3Simulating Urban Growth with Brownian Agents326
8.3.4Results of Computer Simulations: Berlin329
9.Economic Agglomeration335
9.1Migration and Agglomeration of Workers335
9.1.1Spatial Economic Patterns335
9.1.2Model Equations for Migration and Employment337
9.1.3Derivation of a Competition Dynamics341
9.2Dynamic Model of Economic Concentration345
9.2.1Production Function and Transition Rates345
9.2.2Simulation of Spatial Economic Agglomeration350
10.Spatial Opinion Structures in Social Systems357
10.1Quantitative Sociodynamics357
10.1.2Stochastic Changes and Transition Rates359
10.2Collective Opinion Formation of Brownian Agents363
10.2.1Dynamic Equations363
10.2.2Subpopulation Sizes in a System with Fast Communication366
10.2.3Influence of External Support369
10.2.4Critical Conditions for Spatial Opinion Separation371
10.3Spatial Opinion Patterns in a Model of Direct Interactions375
10.3.1Transition Rates and Mean Value Equations375
10.3.2Stationary Solutions for a Single Box379
10.3.3Results of Computer Simulations382

Back Back to Front Page