POINCARE CHAOS FOR A HYPERBOLIC QUASILINEAR SYSTEM

AKHMET M., Fen M. O., Tleubergenova M., Zhamanshin A.

MISKOLC MATHEMATICAL NOTES, vol.20, no.1, pp.33-44, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.18514/mmn.2019.2826
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.33-44
  • Keywords: hyperbolic quasilinear systems, Poincare chaos, unpredictable solutions
  • Middle East Technical University Affiliated: Yes

Abstract

The existence of unpredictable motions in systems of quasilinear differential equations with hyperbolic linear part is rigorously proved. We make use of the topology of uniform convergence on compact sets and the contraction mapping principle to prove the existence of unpredictable motions. Appropriate examples with simulations that support the theoretical results are provided.