Research output: Contribution to journal › Article › peer-review
In this paper, it is shown numerically that a class of fractional-order piece-wise continuous systems, which depend on a single real bifurcation parameter, have no zero Lyapunov exponents but can be chaotic or hyperchaotic with hidden attractors. Although not analytically proved, this conjecture is verified on several systems including a fractional-order piece-wise continuous hyperchaotic system, a piece-wise continuous chaotic Chen system, a piece-wise continuous variant of the chaotic Shimizu-Morioka system and a piece-wise continuous chaotic Sprott system. These systems are continuously approximated based on results of differential inclusions and selection theory, and numerically integrated with the Adams-Bashforth-Moulton method for fractional-order differential equations. It is believed that the obtained results are valid for many, if not most, fractional-order PWC systems.
Original language | English |
---|---|
Pages (from-to) | 1061-1078 |
Number of pages | 18 |
Journal | Nonlinear Dynamics |
Volume | 92 |
Issue number | 3 |
DOIs | |
State | Published - 1 May 2018 |
ID: 35268554