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Bifurcation and chaos in the fractional form of Hénon-Lozi type map
Ouannas A., Khennaoui A.–A., Wang X., Pham V.-T., Boulaaras S.,
Published in Springer Science and Business Media Deutschland GmbH
2020
Volume: 229
   
Issue: 12-13
Pages: 2261 - 2273
Abstract
In this paper, we are particularly interested in the fractional form of the Hénon-Lozi type map. Using discrete fractional calculus, we show that the general behavior of the proposed fractional order map depends on the fractional order. The dynamical properties of the new generalized map are investigated by applying numerical tools such as: phase portrait, bifurcation diagram, largest Lyapunov exponent, and 0-1 test. It shows that the fractional order Hénon-Lozi map exhibits a range of different dynamical behaviors including chaos and coexisting attractors. Furthermore, a one-dimensional control law is proposed to stabilize the states of the fractional order map. Numerical results are presented to illustrate the findings. © 2020, EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.
About the journal
JournalData powered by TypesetEuropean Physical Journal: Special Topics
PublisherData powered by TypesetSpringer Science and Business Media Deutschland GmbH
ISSN19516355
Open AccessNo