Influence of Spatial Inhomogeneity on the Formation of Chaotic Modes at the Self-Organization Process

  • Z. M. Liashenko Sumy State University
  • I. A. Lyashenko Sumy State University, Technische Universit¨at Berlin, Institut f¨ur Mechanik, FG Systemdynamik und Reibungsphysik
Keywords: self-organization, Lorenz system, strange attractor, order parameter, partial differential equations


The Lorentz system of equations, in which gradient terms are taken into account, has been solved numerically. Three fundamentally different modes of evolution are considered. In the first mode, the spatial distribution of the order parameter permanently changes in time, and domains of two types with positive and negative order parameter values are formed. In the second mode, the order parameter distribution is close to the stationary one. Finally, in the third mode, the order parameter is identical over the whole space. The dependences of the average area of domains, their number, and their total area on the time are calculated in the first two cases. In the third case, the contribution of gradient terms completely vanishes, and a classical Lorenz attractor is realized.


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How to Cite
Liashenko, Z., & Lyashenko, I. (2020). Influence of Spatial Inhomogeneity on the Formation of Chaotic Modes at the Self-Organization Process. Ukrainian Journal of Physics, 65(2), 130.
General physics