Abstract
We consider swarms as systems with partial random synchronicity and look at the conditions for their convergence to a fixed point. The conditions turn out to be not much more stringent than for linear, one-step, stationary iterative schemes, either synchronous or sequential. The rate of convergence is also comparable. The main result is that swarms converge in cases when synchronous and/or sequential updating systems do not. The other significant result is that swarms can undergo a transition from non convergence to convergence as their degree of partial synchronicity diminishes, i.e., as they get more “disordered”. The production of order by disordered action appears as a basic characteristic of swarms.
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References
Beni, G., Wang, J.: Swarm Intelligence. In: Proc. 7th Ann. Meeting of the Robotics Society of Japan (in Japanese), pp. 425–428 (1989)
Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Oxford Univ. Press, New York (1999)
Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kauffman, San Mateo (2001)
Parrish, J.K., Hamner, W.M. (eds.): Animal Groups in Three Dimensions. Cambridge University Press, Cambridge (1997)
Camazine, S., Deneubourg, J.-L., Franks, N.R., Sneyd, J., Theraulaz, G., Bonabeau, E.: Self-Organization in Biological Systems. Princeton Univ. Press, Princeton (2001)
Liu, Y., Passino, K.M., Polycarpou, M.M.: Stability analysis of one-dimensional asynchronous swarms. In: Proc. Amer. Contr.Conf., Arlington, VA, pp. 716–721 (2001)
Liu, Y., Passino, K.M., Polycarpou, M.M.: Stability analysis of one-dimensional asynchronous mobile swarms. In: Proc.Conf. Decision Contr., Orlando, FL, pp. 1077–1082 (2001)
Liu, Y., Passino, K.M., Polycarpou, M.M.: Stability analysis of one-dimensional asynchronous swarms. IEEE Trans. Automat. Contr. 48, 1848–1854 (2003)
Gazi, V., Passino, K.M.: Stability of a one-dimensional discrete-time asynchronous swarm. In: Proc.Joint IEEE Int. Symp. Intell. Contr./IEEE Conf. Contr.Appl., Mexico City, Mexico, pp. 19–24 (2001)
Gazi, V., Passino, K.M.: Stability Analysis of Social Foraging Swarms. IEEE Trans.Syst. Man and Cybern. B 34, 539–557 (2004)
Liang, P., Beni, G.: Robotic Morphogenesis. In: Proc. Int. Conf. Robotics and Automation, vol. 2, pp. 2175–2180 (1995)
Turing, A.M.: The Chemical Basis for Morphogenesis. Phil. Trans. Royal Soc. London B 237, 37–72 (1952)
Beni, G.: Research Perspectives in Swarm Intelligence: the reconfiguration problem. In: Proc. Int. Symposium on System Life, Tokyo, Japan, July 21-22 (1997)
Beni, G.: Distributed Robotic Systems and Swarm Intelligence. Journal of the Robot Society of Japan (in Japanese) 10, 31–37 (1992)
Beni, G., Hackwood, S.: Stationary Waves in Cyclic Swarms. In: Proc. IEEE Int. Symposium on Intelligent Control, Glasgow, pp. 234–242 (1992)
Beni, G., Liang, P.: Pattern Reconfiguration in Swarms-Convergence of a Distributed Asynchronous and Bounded Iterative Algorithm. IEEE Trans. Robotics and Autom. 12, 485–490 (1996)
Axelsson, O.: Iterative Solution Methods. Cambridge University Press, Cambridge (1994)
Bertsekas, D.P., Tsitsiklis, J.N.: Parallel and Distributed Computation, Englewood Cliffs, N.J. (1999)
Huang, Q., Beni, G.: Stationary Waves in 2 Dimensional Cyclic Swarms. In: IEEE/TSJ International Conference on Intelligent Robots and Systems, Yokohama, Japan, pp. 433–440 (1993)
Young, D.M.: Iterative Solutions of Large Linear Systems. Academic Press, London (1971)
Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis, 2nd edn. Springer, Heidelberg (1971)
Tel, G.: Introduction to Distributed Algorithms. Cambridge University Press, Cambridge (1994)
Barnsley, M.: Fractals Everywhere. Academic Press, New York (1988)
Elton, J.: An Ergodic Theorem for Iterated Maps. Journal of Ergodic Theory and Dynamical Systems 7, 481–488 (1987)
Wolfram, S.: A New Kind of Science. p. 591 Wolfram Media,(2002)
Schonfisch, B., de Roos, A.: Synchronous and Asynchronous Updating in Cellular Automata. Biosystems 51, 123–143 (1999)
Bersini, H., Detours, V.: Asynchrony induces stability in cellular automata based models. In: Brooks, R.A., Maes, P. (eds.) Artificial Life IV, pp. 382–387. MIT Press, MA (1994)
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Beni, G. (2005). Order by Disordered Action in Swarms. In: Şahin, E., Spears, W.M. (eds) Swarm Robotics. SR 2004. Lecture Notes in Computer Science, vol 3342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30552-1_13
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DOI: https://doi.org/10.1007/978-3-540-30552-1_13
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