Modelling of chaos in smooth piecewise dynamical systems with one discontinuous point

Document Type : Original Paper


1 Department of Mathematics, Shhid Beheshti University, Tehran, Iran

2 Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran

3 Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran


In this paper, we provide conditions on the smooth piecewise dynamical systems that guarantee the existence of Devaney chaos. In fact, we show that if f is a generalized semi-baker map with two branches and its derivative greater than or equal √2, then the dynamical system related to that is chaotic in the sense of Devaney. Such conditions on the dynamical systems with more than one discontinues point essentially does not satisfy this result.


Main Subjects

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