Long-time behavior of solutions and chaos in reaction-diffusion equations

Kamal N. Soltanov, Anatolij K. Prykarpatski, Denis Blackmore

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

It is shown that members of a class (of current interest with many applications) of non-dissipative reaction-diffusion partial differential equations with local nonlinearity can have an infinite number of different unstable solutions traveling along an axis of the space variable with varying speeds, traveling impulses and also an infinite number of different states of spatio-temporal (diffusion) chaos. These solutions are generated by cascades of bifurcations governed by the corresponding steady states. The behavior of these solutions is analyzed in detail and, as an example, it is explained how space-time chaos can arise. Results of the same type are also obtained in the case of a nonlocal nonlinearity.

Original languageEnglish (US)
Pages (from-to)91-100
Number of pages10
JournalChaos, Solitons and Fractals
Volume99
DOIs
StatePublished - Jun 1 2017

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

Keywords

  • Behavior of solutions
  • Chaos
  • Reaction-diffusion equation
  • Semilinear PDE

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