Multistability, Chaos, and Synchronization in Novel Symmetric Difference Equation

This paper presents a new third-order symmetric difference equation transformed into a 3D discrete symmetric map. The nonlinear dynamics and symmetry of the proposed map are analyzed with two initial conditions for exploring the sensitivity of the map and highlighting the influence of the map parame...

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Bibliographic Details
Published in:Symmetry (Basel) 2024-08, Vol.16 (8), p.1093
Main Authors: Othman Abdullah Almatroud, Ma’mon Abu Hammad, Dababneh, Amer, Diabi, Louiza, Ouannas, Adel, Khennaoui, Amina Aicha, Alshammari, Saleh
Format: Article
Language:English
Subjects:
Asymmetry
Behavior
Bifurcations
chaos
control
difference equation
Difference equations
Eigenvalues
fixed point
Initial conditions
Liapunov exponents
multistability
Neural networks
Nonlinear control
Nonlinear dynamics
Parameter sensitivity
Physics
symmetric map
Symmetry
Synchronism
Two dimensional analysis
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Summary:This paper presents a new third-order symmetric difference equation transformed into a 3D discrete symmetric map. The nonlinear dynamics and symmetry of the proposed map are analyzed with two initial conditions for exploring the sensitivity of the map and highlighting the influence of the map parameters on its behaviors, thus comparing the findings. Moreover, the stability of the zero fixed point and symmetry are examined by theoretical analysis, and it is proved that the map generates diverse nonlinear traits comprising multistability, chaos, and hyperchaos, which is confirmed by phase attractors in 2D and 3D space, Lyapunov exponents (LEs) analysis and bifurcation diagrams; also, 0-1 test and sample entropy (SampEn) are used to confirm the existence and measure the complexity of chaos. In addition, a nonlinear controller is introduced to stabilize the symmetry map and synchronize a duo of unified symmetry maps. Finally, numerical results are provided to illustrate the findings.
ISSN:2073-8994
DOI:10.3390/sym16081093