Existence of Unpredictable Solutions and Chaos
Chaotic Dynamics
2016-02-09 v1 Dynamical Systems
Abstract
In paper [1] unpredictable points were introduced based on Poisson stability, and this gives rise to the existence of chaos in the quasi-minimal set. This time, an unpredictable function is determined as an unpredictable point in the Bebutov dynamical system. The existence of an unpredictable solution and consequently chaos of a quasi-linear system of ordinary differential equations are verified. This is the first time that the description of chaos is initiated from a single function, but not on a collection of them. The results can be easily extended to different types of differential equations. An application of the main theorem for Duffing equations is provided.
Keywords
Cite
@article{arxiv.1602.02614,
title = {Existence of Unpredictable Solutions and Chaos},
author = {Marat Akhmet and Mehmet Onur Fen},
journal= {arXiv preprint arXiv:1602.02614},
year = {2016}
}
Comments
15 pages, 4 figures