Self-organized pattern formation in a swarm system as a transient phenomenon of non-linear dynamics

This article presents a microscopic model (agent positions, directions and interactions are explicitly modelled) of mobile agents (or self-propelled particles) that is inspired by the ‘complex transport networks’ reported by Jones (2010; The emergence and dynamical evolution of complex transport networks from simple low-level behaviours, International Journal of Unconventional Computing 6, pp. 125–144). Here, the agents' positions are modelled continuously. This multi-agent system (or artificial swarm) shows a wide variety of self-organized pattern formations. The self-organization is based on the non-linearity of the agents' turns (discrete jumps in the agents' directions) and the indirect interactions of the agents via a potential field that determines their motion (high values are attractive) and which is changed by themselves (agents increase the value of the potential field at their positions). At least most of the irregular and complex patterns are transient. The patterns found during the transient are more complex than those the system converges to. Still, this transient behaviour is relevant. We empirically investigate the transient times in dependence of several system parameters and give examples.

[1]  Jeff Jones,et al.  The Emergence and Dynamical Evolution of Complex Transport Networks from Simple Low-Level Behaviours , 2015, Int. J. Unconv. Comput..

[2]  Marco Dorigo,et al.  Swarm intelligence: from natural to artificial systems , 1999 .

[3]  Mauro Birattari,et al.  Swarm Intelligence , 2012, Lecture Notes in Computer Science.

[4]  Maximino Aldana,et al.  Phase Transitions in Self-Driven Many-Particle Systems and Related Non-Equilibrium Models: A Network Approach , 2003 .

[5]  G. Ruxton,et al.  Spatial self-organization and persistence of transients in a metapopulation model , 1996, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[6]  H. Jaeger,et al.  The Physics of Granular Materials , 1996 .

[7]  Vijay Narayan,et al.  Long-Lived Giant Number Fluctuations in a Swarming Granular Nematic , 2007, Science.

[8]  B. Werner,et al.  Self-Organization of Sorted Patterned Ground , 2003, Science.

[9]  Heiko Hamann,et al.  Space-Time Continuous Models of Swarm Robotic Systems - Supporting Global-to-Local Programming , 2010, Cognitive Systems Monographs.

[10]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[11]  W. Rappel,et al.  Self-organization in systems of self-propelled particles. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  金子 邦彦.  Theory and applications of coupled map lattices , 1993 .

[13]  I. Prigogine,et al.  The end of certainty : time, chaos, and the new laws of nature , 1997 .

[14]  A. Mikhailov,et al.  Noise-induced breakdown of coherent collective motion in swarms. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  Frank Schweitzer,et al.  Brownian Agent Models for Swarm and Chemotactic Interaction Brownian Agents , 2002 .

[16]  Lutz Schimansky-Geier,et al.  Structure formation by active Brownian particles , 1995 .

[17]  Crutchfield,et al.  Are attractors relevant to turbulence? , 1988, Physical review letters.

[18]  F. Schweitzer.  Brownian Agents and Active Particles , 2003, Springer Series in Synergetics.

[19]  S. Levin,et al.  Diffusion and Ecological Problems: Modern Perspectives , 2013 .

[20]  K. Painter,et al.  Volume-filling and quorum-sensing in models for chemosensitive movement , 2002 .

[21]  J. Deneubourg,et al.  The self-organizing exploratory pattern of the argentine ant , 1990, Journal of Insect Behavior.

[22]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[23]  Xin Chen,et al.  Modeling and simulation of swarms for collecting objects , 2006, Robotica.

[24]  N. Nilsson.  STUART RUSSELL AND PETER NORVIG, ARTIFICIAL INTELLIGENCE: A MODERN APPROACH , 1996 .

[25]  Ying-Cheng Lai,et al.  Chaotic transients in spatially extended systems , 2008 .

[26]  A. Barabasi,et al.  Collective Motion of Self-Propelled Particles: Kinetic Phase Transition in One Dimension , 1997, cond-mat/9712154.

[27]  Dirk Helbing,et al.  Active Walker Model for the Formation of Human and Animal Trail Systems , 1997 .

[28]  Ling Li,et al.  Emergent Specialization in Swarm Systems , 2002, IDEAL.

[29]  Thomas Hillen,et al.  Metastability in Chemotaxis Models , 2005 .

[30]  Craig W. Reynolds.  Flocks, herds, and schools: a distributed behavioral model , 1987, SIGGRAPH.

[31]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[32]  J. V. Rauff,et al.  Multi-Agent Systems: An Introduction to Distributed Artificial Intelligence , 2005 .

[33]  A. Hastings.  Transients: the key to long-term ecological understanding? , 2004, Trends in ecology & evolution.

[34]  Jacques Ferber,et al.  Multi-agent systems - an introduction to distributed artificial intelligence , 1999 .

[35]  A. Ōkubo,et al.  MODELLING SOCIAL ANIMAL AGGREGATIONS , 1994 .

[36]  Guy Theraulaz,et al.  Phase-ordering kinetics of cemetery organization in ants , 1998 .

[37]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[38]  A. Hastings.  Transient dynamics and persistence of ecological systems , 2001 .

[39]  L. Edelstein-Keshet.  Mathematical models of swarming and social aggregation , .

[40]  Stephen Wolfram,et al.  A New Kind of Science , 2003, Artificial Life.

[41]  T. Schmickl,et al.  INDIVIDUAL BASED MODELLING OF TEMPERATURE INDUCED AGGREGATION BEHAVIOUR , 2009 .

[42]  Vicsek,et al.  Lattice-gas model for collective biological motion. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[43]  A. Drogoul,et al.  Multi-Agent Simulation as a Tool for Modeling Societies: Application to Social Differentiation in Ant Colonies , 1992, MAAMAW.

[44]  A. Hastings,et al.  Persistence of Transients in Spatially Structured Ecological Models , 1994, Science.

[45]  Bastien Chopard,et al.  Cellular Automata and Lattice Boltzmann Techniques: an Approach to Model and Simulate Complex Systems , 2002, Adv. Complex Syst..

[46]  A. Ōkubo.  Dynamical aspects of animal grouping: swarms, schools, flocks, and herds. , 1986, Advances in biophysics.

[47]  Jeff Jones,et al.  Characteristics of Pattern Formation and Evolution in Approximations of Physarum Transport Networks , 2010, Artificial Life.