Existence of unpredictable solutions and chaos

Authors: MARAT AKHMET, MEHMET ONUR FEN

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

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