The New Four-Dimensional Fractional Chaotic Map with Constant and Variable-Order: Chaos, Control and Synchronization

Using fractional difference equations to describe fractional and variable-order maps, this manuscript discusses the dynamics of the discrete 4D sinusoidal feedback sine iterative chaotic map with infinite collapse (ICMIC) modulation map (SF-SIMM) with fractional-order. Also, it presents a novel vari...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-10, Vol.11 (20), p.4332
Main Authors: Hamadneh, Tareq, Ahmed, Souad Bensid, Al-Tarawneh, Hassan, Alsayyed, Omar, Gharib, Gharib Mousa, Al Soudi, Maha S., Abbes, Abderrahmane, Ouannas, Adel
Format: Article
Language:English
Subjects:
Algorithms
Behavior
C0 complexity
Calculus
chaos
Chaos theory
Controllers
Difference equations
Discrete systems
dynamical behavior
Fourier transforms
Iterative methods
largest Lyapunov exponents
Liapunov exponents
Neural networks
Numerical methods
Synchronism
variable fractional-order
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Summary:Using fractional difference equations to describe fractional and variable-order maps, this manuscript discusses the dynamics of the discrete 4D sinusoidal feedback sine iterative chaotic map with infinite collapse (ICMIC) modulation map (SF-SIMM) with fractional-order. Also, it presents a novel variable-order version of SF-SIMM and discusses their chaotic dynamic behavior by employing a distinct function for the variable fractional-order. To establish the existence of chaos in the suggested discrete SF-SIMM, some numerical methods such as phase plots, bifurcation and largest Lyapunov exponent diagrams, C0 complexity and 0–1 test are utilized. After that, two different control schemes are used for the conceived discrete system. The states are stabilized and asymptotically forced towards zero by the first controller. The second controller is used to synchronize a pair of maps with non–identical parameters. Finally, MATLAB simulations will be executed to confirm the results provided.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11204332