The Effect of Caputo Fractional Variable Difference Operator on a Discrete-Time Hopfield Neural Network with Non-Commensurate Order

In this work, we recall some definitions on fractional calculus with discrete-time. Then, introduce a discrete-time Hopfield neural network (D.T.H.N.N) non-commensurate 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 variable order has chaotic behavior. Furthermore, use 0-1 test C0 complexity algorithm confirm prove results obtained about presence of chaos. Finally, simulations carried out in Matlab illustrate results.