Bifurcation and chaos in the fractional form of Hénon-Lozi type map

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 investi...

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Bibliographic Details
Published in:The European physical journal. ST, Special topics Special topics, 2020-09, Vol.229 (12-13), p.2261-2273
Main Authors: Ouannas, Adel, Khennaoui, Amina–Aicha, Wang, Xiong, Pham, Viet-Thanh, Boulaaras, Salah, Momani, Shaher
Format: Article
Language:English
Subjects:
Atomic
Bifurcations
Chaos theory
Classical and Continuum Physics
Condensed Matter Physics
Fractional calculus
Liapunov exponents
Materials Science
Measurement Science and Instrumentation
Molecular
Nonlinear and Complex Physics
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
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Summary: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.
ISSN:1951-6355
1951-6401
DOI:10.1140/epjst/e2020-900193-4