Models and Applications of Organism Transportation

  • Atsushi Tero
Part of the Mathematics for Industry book series (MFI, volume 5)


Organism makes various transportation networks. These many networks have adaptive character, in which the link grows with high-use and degenerates with low-use. In this chapter the mathematical model of adaptive network is introduced. Next, this chapter shows the simulation results by this mathematical model with various parameter. As a result, this chapter shows that how the organism can gain the global function only with the local growth law.


Adaptive network Mathematical model Optimal network Shortest path True slime mold 



I would like to express my gratitude to joint researchers Professor Toshiyuki Nakagaki (Future University Hakodate), Professor Seiji Takagi (Hokkaido University), and Professor Toru Saigusa (Kyushu University) who provided experimental data for this research, as well as Professor Ryo Kobayashi (Hiroshima University) for assisting us with consultation on mathematical models.


  1. 1.
    L.E. Sieburth, Auxin is required for leaf vein pattern in arabidopsis. Plant Phys. 121, 1179–1190 (1999)Google Scholar
  2. 2.
    T. Nakagaki, H. Yamada, A. Tóth, Maze-solving by an amoeboid organism. Nature 407, 470 (2000)Google Scholar
  3. 3.
    A. Tero, R. Kobayashi, T. Nakagaki, A mathematical model for adaptive transport network in path finding by the true slime mold. J. Theor. Biol. 244, 553–564 (2007) (ELSEVIER)Google Scholar
  4. 4.
    A. Tero, R. Kobayashi, T. Nakagaki, Physarum solver: a biologically inspired method of road-network navigation. Phys. A 363, 115–119 (2006) (ELSEVIER)Google Scholar
  5. 5.
    T. Miyaji, I. Ohnishi, Physarum can solve the shortest path problem on riemannian surface mathematically rigorously. Int. J. Pure Appl. Math. 47(3), 353–369 (2008)Google Scholar
  6. 6.
    V. Bonifaci, K. Mehlhorn, G. Varma, Physarum can compute shortest paths. J. Theor. Biol. 309, 121–133 (2012)Google Scholar
  7. 7.
    T. Nakagaki, T. Saigusa, A. Tero, R. Kobayashi, Effects of Amount of Food on Path Selection in the Transport Network of an Amoeboid Organism. Topological Aspects of Critical Systems and Networks, 2007/07 pp. 94–100Google Scholar
  8. 8.
    A. Tero, K. Toyabe, K. Yumiki, R. Kobayashi, T. Nakagaki, A method inspired by Physarum for solving the Steiner problem. Int. J. Unconventional Comput. 6, 109–123 (2010)Google Scholar
  9. 9.
    A. Tero, S. Takagi, T. Saigusa, K. Ito, D.P. Bebber, M.D. Fricker, K. Yumiki, R. Kobayashi, T. Nakagaki, Rules for biologically inspired adaptive network design. Science 327(5964), 439–442 (2010/1/22)Google Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Institute of Mathematics for IndustryKyushu UniversityFukuokaJapan

Personalised recommendations