Paper Info
Title
Chaotic Behavior Analysis of a New Incommensurate Fractional-Order Hopfield Neural Network System
Abstract
This study intends to examine different dynamics of the chaotic incommensurate fractional-order Hopfield neural network model. The stability of the proposed incommensurate-order model is analyzed numerically by continuously varying the values of the fractional-order derivative and the values of the system parameters. It turned out that the formulated system using the Caputo differential operator exhibits many rich complex dynamics, including symmetry, bistability, and coexisting chaotic attractors. On the other hand, it has been detected that by adapting the corresponding controlled constants, such systems possess the so-called offset boosting of three variables. Besides, the resultant periodic and chaotic attractors can be scattered in several forms, including 1D line, 2D lattice, and 3D grid, and even in an arbitrary location of the phase space. Several numerical simulations are implemented, and the obtained findings are illustrated through constructing bifurcation diagrams, computing Lyapunov exponents, calculating Lyapunov dimensions, and sketching the phase portraits in 2D and 3D projections.
Year
DOI
Venue
2021
10.1155/2021/3394666
COMPLEXITY
DocType
Volume
ISSN
Journal
2021
1076-2787
Citations 
PageRank 
References 
0
0.34
0
Authors
8
Name
Order
Citations
PageRank
Nadjette Debbouche100.68
Adel Ouannas200.34
Iqbal M. Batiha300.34
Giuseppe Grassi443.68
Mohammed K. A. Kaabar500.68
Hadi Jahanshahi614.07
Ayman A. Aly703.04
Awad M. Aljuaid800.68