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Existence of Unpredictable Solutions and Chaos

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.

preprint2016arXivOpen access
Marat AkhmetMehmet Onur Fen
math.DSnlin.CD
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Marat AkhmetMehmet Onur Fen

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