Robust Swarm Model Based on Mutual Anticipation: Swarm as a Mobile Network Analyzed by Rough Set Lattice

Robust Swarm Model Based on Mutual Anticipation: Swarm as a Mobile Network Analyzed by Rough Set Lattice

Yukio-Pegio Gunji (Kobe University, Japan), Hisashi Murakami (Kobe University, Japan), Takayuki Niizato (Kobe University, Japan), Yuta Nishiyama (Kobe University, Japan), Takenori Tomaru (Kobe University, Japan) and Andrew Adamatzky (University of the West of England, UK)
Copyright: © 2012 |Pages: 14
DOI: 10.4018/jalr.2012010105
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Abstract

The authors propose a novel model for a swarm in which inherent noise positively contribute to generate a swarm. In the authors’ model diverse behaviors of individuals are mutually anticipated to give rise to robust collective behavior. Because a swarm is generated due to inherent perturbation, a swarm can be maintained even under highly perturbed conditions. Thus, the model reveals robust rather than stable collective behavior. The authors elaborate behavior of the model with respect to density and polarization. The authors show that mutual anticipation structure can be expressed as a fixed point with respect to a particular operation derived by equivalence relation, a collection of the fixed points can form a particular algebraic structure, called a lattice, and a swarm as a mobile network can be characterized by the structure of a lattice.
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2. Robustness Vs. Stability

Signal and/or information in living system must be robust since they are always exposed in strong perturbation. First of all, we refer to the difference between robustness and stability. We refer the term stability to the case in which the force to keep order is against perturbation, and the term robustness to the case in which perturbation positively contribute to keep order. In other words, the order in a stable system is achieved by removing perturbation. The order in a robust system is achieved by cooperation of the inherent mechanism of the system and perturbation.

Most systems described in physics are stable systems but not robust systems. After removing the external force, the body is relaxed and recovered to the stable state. Soon after a planet is taken away from its own orbit, it turns to the original orbit again. The essential property of a dynamical system is estimated by the degree of separation from an original orbit triggered by perturbation, known as Lyapunov exponent. It shows how stability is only privileged in dynamical systems (Rosenstein, Collins, & De Luca, 1993).

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