Derivation of a Micro-Macro Link for Collective Decision-Making Systems
Relating microscopic features (individual level) to macroscopic features (swarm level) of self-organizing collective systems is challenging. In this paper, we report the mathematical derivation of a macroscopic model starting from a microscopic one for the example of collective decision-making. The collective system is based on the application of a majority rule over groups of variable size which is modeled by chemical reactions (micro-model). From an approximated master equation we derive the drift term of a stochastic differential equation (macro-model) which is applied to predict the expected swarm behavior. We give a recursive definition of the polynomials defining this drift term. Our results are validated by Gillespie simulations and simulations of the locust alignment.
KeywordsMaster Equation Reaction Schema Majority Rule Neighborhood Size Markov Chain Monte Carlo Method
Unable to display preview. Download preview PDF.
- 2.Schweitzer, F.: Brownian Agents and Active Particles. On the Emergence of Complex Behavior in the Natural and Social Sciences. Springer, Berlin (2003)Google Scholar
- 3.Alexander, J.C., Giesen, B., Münch, R., Smelser, N.J. (eds.): The Micro-Macro Link. University of California Press, Berkeley (1987)Google Scholar
- 5.Hamann, H.: Space-Time Continuous Models of Swarm Robotics Systems: Supporting Global-to-Local Programming. Springer, Berlin (2010)Google Scholar
- 8.Berman, S., Kumar, V., Nagpal, R.: Design of control policies for spatially inhomogeneous robot swarms with application to commercial pollination. In: LaValle, S., et al. (eds.) IEEE Int. Conf. on Robotics and Automation, ICRA 2011, pp. 378–385. IEEE Press (2011)Google Scholar
- 9.Huepe, C., Zschaler, G., Do, A.L., Gross, T.: Adaptive-network models of swarm dynamics. New Journal of Physics 13(7), 073022 (2011)Google Scholar
- 13.Valentini, G., Hamann, H., Dorigo, M.: Self-organized collective decision making: The weighted voter model. In: Lomuscio, A., et al. (eds.) Proc. of the 13th Int. Conf. on Autonomous Agents and Multiagent Systems, AAMAS 2014, pp. 45–52 (2014)Google Scholar
- 14.Biancalani, T., Dyson, L., McKane, A.J.: Noise-induced bistable states and their mean switching time in foraging colonies. Phys. Rev. Lett. 112, 038101 (2014)Google Scholar
- 15.van Kampen, N.G.: Stochastic processes in physics and chemistry. North-Holland, Amsterdam (1981)Google Scholar