Artificial Life and Robotics

, Volume 12, Issue 1–2, pp 29–32 | Cite as

Mathematical modeling of frogs’ calling behavior and its possible application to artificial life and robotics

  • Ikkyu Aihara
  • Hiroyuki Kitahata
  • Kenichi Yoshikawa
  • Kazuyuki Aihara
Original Article


This paper theoretically and qualitatively describes the calling behavior of the Japanese tree frog Hyla japonica with a simple model of phase oscillators. Experimental analysis showed that while an isolated single male frog called nearly periodically, two interacting male frogs called periodically but alternately, with little overlap. We model these phenomena as a system of coupled phase oscillators, where each isolated oscillator behaves periodically as a model of the calling of a single frog, and two coupled oscillators show antiphase synchronization, reflecting the alternately calling behavior of two interacting frogs. Then, we extend the model to a system of three coupled oscillators virtually corresponding to three interacting male frogs, and analyse the nonlinear dynamics and the bifurcation. We also discuss the biological meaning of the calling behavior and its possible application to artificial life and robotics.

Key words

Calling behavior Frogs Synchronization Oscillators Bifurcation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Winfree AT (1967) Biological rhythms and the behavior of population of coupled oscillators. J Theor Biol 16:15–42CrossRefGoogle Scholar
  2. 2.
    Kuramoto Y (1984) Chemical oscillations, waves, and turbulence. Springer, BerlinMATHGoogle Scholar
  3. 3.
    Ermentrout GB, Rinzel J (1984) Beyond a pacemaker’s entrainment limit: phase walk-through. Am J Physiol 246:102–106Google Scholar
  4. 4.
    Mirollo RE, Strogatz SH (1990) Synchronization of pulse-coupled biological oscillators. Siam J Appl Math 50:1645–1662MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Strogatz SH (1994) Nonlinear dynamics and chaos. Perseus, CambridgeGoogle Scholar
  6. 6.
    Hoppensteadt FC, Izhikevich EM (1997) Weakly connected neural networks. Springer, New YorkGoogle Scholar
  7. 7.
    Pikovsky A, Rosenblum M, Kurth J (2001) Synchronization: a universal concept in nonlinear sciences. Cambridge University Press, CambridgeMATHGoogle Scholar
  8. 8.
    Loftus-Hills JJ (1974) Analysis of an acoustic pacemaker in Strecker’s chorus frog Pseudacris streckeri (Anura:Hyli-dae). J Comp Physiol 90:75–87CrossRefGoogle Scholar
  9. 9.
    Lemon RE, Struger J (1980) Acoustic entrainment to randomly generated calls by the frog, Hyla crucifer. J Acoust Soc Am 67:2090–2095CrossRefGoogle Scholar
  10. 10.
    Aihara I, Kitahata H, Horai S, et al. (2006) Synchronization experimentally observed in calling behaviors of Japanese rain frogs (Hyla japonica). Proceedings of the 2006 International Symposium on Nonlinear Theory and its Applications IEICE, pp 767–770Google Scholar
  11. 11.
    Aihara I, Horai S, Kitahata H, et al. (2007) Dynamical calling behaviors experimentally observed in Japanese tree frogs (Hyla japonica). IEICE Trans Fundamentals, E90-A:2154–2161CrossRefGoogle Scholar
  12. 12.
    Matsui M (1996) Natural history of the amphibia (in Japanese). University of Tokyo Press, TokyoGoogle Scholar
  13. 13.
    Iwasawa H, Kuramoto M (1996) Systematic zoology, vol. 9. Vertebrata: Pisces/Amphibia/Reptilia (in Japanese). Nakayama-Shoten, TokyoGoogle Scholar
  14. 14.
    Matsubashi T, Okuyama F (2002) Frogs and toads of Japan + salamander (in Japanese). Yama-Kei Publishers, TokyoGoogle Scholar
  15. 15.
    Yoshimoto M, Yoshikawa K, Mori Y (1993) Coupling among three chemical oscillators: synchronization, phase-death and frustration. Phys Rev E 47:864–874CrossRefGoogle Scholar
  16. 16.
    Miyazaki J, Kinoshita S (2006) Method for determining a coupling function in coupled oscillators with application to Belousov-Zhabotinsky oscillators. Phys Rev E 74:056209CrossRefGoogle Scholar

Copyright information

© International Symposium on Artificial Life and Robotics (ISAROB). 2008

Authors and Affiliations

  • Ikkyu Aihara
    • 1
  • Hiroyuki Kitahata
    • 2
  • Kenichi Yoshikawa
    • 2
  • Kazuyuki Aihara
    • 3
    • 4
  1. 1.Department of Applied Analysis and Complex Dynamical Systems, Graduate School of InformaticsKyoto UniversityKyotoJapan
  2. 2.Department of Physics, Graduate School of ScienceKyoto UniversityKyotoJapan
  3. 3.Institute of Industrial ScienceUniversity of TokyoTokyoJapan
  4. 4.ERATO Aihara Complexity Modelling ProjectJSTTokyoJapan

Personalised recommendations