Coherent Pattern Prediction in Swarms of Delay-Coupled Agents

We consider a general swarm model of self-propelling agents interacting through a pairwise potential in the presence of noise and communication time delay. Previous work has shown that a communication time delay in the swarm induces a pattern bifurcation that depends on the size of the coupling amplitude. We extend these results by completely unfolding the bifurcation structure of the mean field approximation. Our analysis reveals a direct correspondence between the different dynamical behaviors found in different regions of the coupling-time delay plane with the different classes of simulated coherent swarm patterns. We derive the spatiotemporal scales of the swarm structures, as well as demonstrate how the complicated interplay of coupling strength, time delay, noise intensity, and choice of initial conditions can affect the swarm. In particular, our studies show that for sufficiently large values of the coupling strength and/or the time delay, there is a noise intensity threshold that forces a transition of the swarm from a misaligned state into an aligned state. We show that this alignment transition exhibits hysteresis when the noise intensity is taken to be time dependent.

[1]  A. Papachristodoulou,et al.  Synchonization in Oscillator Networks with Heterogeneous Delays, Switching Topologies and Nonlinear Dynamics , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[2]  K. Sneppen,et al.  Time delay as a key to apoptosis induction in the p53 network , 2002, cond-mat/0207236.

[3]  Ira B. Schwartz,et al.  Dynamic coordinated control laws in multiple agent models , 2005, nlin/0510041.

[4]  N. Macdonald Time lags in biological models , 1978 .

[5]  Bo Yang,et al.  Forced consensus in networks of double integrator systems with delayed input , 2010, Autom..

[6]  Necmettin Yildirim,et al.  Modeling operon dynamics: the tryptophan and lactose operons as paradigms. , 2004, Comptes rendus biologies.

[7]  I. Couzin,et al.  Collective memory and spatial sorting in animal groups. , 2002, Journal of theoretical biology.

[8]  D. Grünbaum,et al.  From individuals to aggregations: the interplay between behavior and physics. , 1999, Journal of theoretical biology.

[9]  Dongbing Gu,et al.  Mobile sensor networks for modelling environmental pollutant distribution , 2011, Int. J. Syst. Sci..

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

[11]  R.M. Murray,et al.  Experimental validation of an algorithm for cooperative boundary tracking , 2005, Proceedings of the 2005, American Control Conference, 2005..

[12]  N. Monk Oscillatory Expression of Hes1, p53, and NF-κB Driven by Transcriptional Time Delays , 2003, Current Biology.

[13]  Eric Forgoston,et al.  Noise, bifurcations, and modeling of interacting particle systems , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[14]  Luis Jiménez,et al.  A Multi-agent Architecture for Multi-robot Surveillance , 2009, ICCCI.

[15]  G. F.,et al.  From individuals to aggregations: the interplay between behavior and physics. , 1999, Journal of theoretical biology.

[16]  Michael C. Mackey,et al.  Why the Lysogenic State of Phage λ Is So Stable: A Mathematical Modeling Approach , 2004 .

[17]  Cristina Masoller,et al.  Chaotic maps coupled with random delays: Connectivity, topology, and network propensity for synchronization , 2005, nlin/0512075.

[18]  Eric Forgoston,et al.  Delay-induced instabilities in self-propelling swarms. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Ling Shi,et al.  Virtual attractive-repulsive potentials for cooperative control of second order dynamic vehicles on the Caltech MVWT , 2005, Proceedings of the 2005, American Control Conference, 2005..

[20]  M. Ani Hsieh,et al.  Macroscopic modeling of stochastic deployment policies with time delays for robot ensembles , 2011, Int. J. Robotics Res..

[21]  Joel W. Burdick,et al.  A decentralized motion coordination strategy for dynamic target tracking , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[22]  C Masoller,et al.  Random delays and the synchronization of chaotic maps. , 2005, Physical review letters.

[23]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[24]  John F. Vinsonhaler Birs , 1967 .

[25]  K. Sneppen,et al.  Sustained oscillations and time delays in gene expression of protein Hes1 , 2003, FEBS letters.

[26]  J. Toner,et al.  Flocks, herds, and schools: A quantitative theory of flocking , 1998, cond-mat/9804180.

[27]  Andrea L. Bertozzi,et al.  Multi-Vehicle Flocking: Scalability of Cooperative Control Algorithms using Pairwise Potentials , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[28]  L. Edelstein-Keshet,et al.  Complexity, pattern, and evolutionary trade-offs in animal aggregation. , 1999, Science.

[29]  Andrea L. Bertozzi,et al.  Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups , 2004, SIAM J. Appl. Math..

[30]  W. Marsden I and J , 2012 .

[31]  E. W. Justh,et al.  Steering laws and continuum models for planar formations , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[32]  Tu,et al.  Long-Range Order in a Two-Dimensional Dynamical XY Model: How Birds Fly Together. , 1995, Physical review letters.

[33]  Jeff Moehlis,et al.  Novel Vehicular Trajectories for Collective Motion from Coupled Oscillator Steering Control , 2008, SIAM J. Appl. Dyn. Syst..

[34]  Leah Edelstein-Keshet,et al.  Do travelling band solutions describe cohesive swarms? An investigation for migratory locusts , 1998 .

[35]  Helbing,et al.  Social force model for pedestrian dynamics. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[36]  Sven Koenig,et al.  Trail-laying robots for robust terrain coverage , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[37]  Lutz Schimansky-Geier,et al.  Swarming in three dimensions. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  H Larralde,et al.  Phase transitions in systems of self-propelled agents and related network models. , 2007, Physical review letters.

[39]  M. Mackey,et al.  Bifurcations in a white-blood-cell production model. , 2004, Comptes rendus biologies.

[40]  Randy A. Freeman,et al.  Decentralized Environmental Modeling by Mobile Sensor Networks , 2008, IEEE Transactions on Robotics.

[41]  P. Holmes,et al.  The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model , 1982, Journal of mathematical biology.

[42]  H. Berg,et al.  Dynamics of formation of symmetrical patterns by chemotactic bacteria , 1995, Nature.

[43]  Naomi Ehrich Leonard,et al.  Virtual leaders, artificial potentials and coordinated control of groups , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).