2016/02/08 by Akhmet, Marat, Fen, Mehmet Onur
#Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences
paper · doi:10.48550/arxiv.1602.02614
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.