Existence of unpredictable solutions and chaos

Authors

MARAT AKHMET
MEHMET ONUR FEN

DOI

10.3906/mat-1603-51

Abstract

Recently we introduced the concept of Poincaré chaos. In the present paper, by means of the Bebutov dynamical system, an unpredictable solution is considered as a generator of the chaos in a quasilinear system. The results can be easily extended to different types of differential equations. An example of an unpredictable function is provided. A proper irregular behavior in coupled Duffing equations is observed through simulations.

Keywords

Poincaré chaos, unpredictable function, Poisson stability, Bebutov dynamical system, quasilinear differential equation, chaos control

First Page

254

Last Page

266

Recommended Citation

AKHMET, MARAT and FEN, MEHMET ONUR (2017) "Existence of unpredictable solutions and chaos," Turkish Journal of Mathematics: Vol. 41: No. 2, Article 4. https://doi.org/10.3906/mat-1603-51
Available at: https://journals.tubitak.gov.tr/math/vol41/iss2/4