The Effect of Caputo Fractional Variable Difference Operator on a Discrete-Time Hopfield Neural Network with Non-Commensurate Order
Rabia Chaimaà Karoun, Adel Ouannas, Mohammed Al Horani, Giuseppe Grassi
Abstract
In this work, we recall some definitions on fractional calculus with discrete-time. Then, we introduce a discrete-time Hopfield neural network (D.T.H.N.N) with non-commensurate fractional variable-order (V.O) for three neurons. After that, phase-plot portraits, bifurcation and Lyapunov exponents diagrams are employed to verify that the proposed discrete time Hopfield neural network with non-commensurate fractional variable order has chaotic behavior. Furthermore, we use the 0-1 test and C0 complexity algorithm to confirm and prove the results obtained about the presence of chaos. Finally, simulations are carried out in Matlab to illustrate the results.
Topics & Concepts
Phase portraitArtificial neural networkChaoticVariable (mathematics)Discrete time and continuous timeFractional calculusMathematicsLyapunov exponentHopfield networkMATLABBifurcationApplied mathematicsControl theory (sociology)Computer scienceMathematical analysisArtificial intelligencePhysicsNonlinear systemQuantum mechanicsOperating systemControl (management)StatisticsNeural Networks and ApplicationsChaos control and synchronizationFractional Differential Equations Solutions