Diffusive waves, dynamical stabilization and spatio-temporal chaos in a community of three competitive species

  • Sergei Petrovskii
  • Kohkichi Kawasaki
  • Fugo Takasu
  • Nanako Shigesada


The spatio-temporal dynamics of three competitive species is considered. Mathematically, the community is described by a system of partial differential equations of Lotka-Volterra type. The properties of the system are investigated both numerically and analytically. We show that for finite initial conditions the dynamics of the system is typically reduced to a succession of travelling diffusive waves, some of which demonstrate rather an unusual behaviour. Particularly, a locally unstable equilibrium can become stable in the wake of a diffusive front. After propagation of the waves, the domain is invaded by irregular spatiotemporal population oscillations that can be classified as spatio-temporal chaos.

Key words

diffusive waves pattern formation spatio-temporal chaos 


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Copyright information

© JJIAM Publishing Committee 2001

Authors and Affiliations

  • Sergei Petrovskii
    • 1
  • Kohkichi Kawasaki
    • 2
  • Fugo Takasu
    • 3
  • Nanako Shigesada
    • 3
  1. 1.Shirshov Institute of OceanologyMoscowRussia
  2. 2.Department of Knowledge Engineering and Computer SciencesDoshisha UniversityKyo-TanabeJapan
  3. 3.Department of Information and Computer SciencesNara Women’s University, Kita-Uoya NishimachiNaraJapan

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