Chaos in The Fractional Variable Order Discrete-Time Neural Networks*

In this paper, a three dimensional discrete time Hopfield neural network with commensurate fractional variable order is presented based on the Caputo like difference operator. The dynamics of the proposed system is investigated by means of chaotic attractors, bifurcation diagram and maximum Lyapunov exponents, It is shown that the discrete time Hopfield neural network has complex behaviour for several fractional variable orders and different system parameter values. Moreover, the approximate entropy and the C
0
complexity algorithms of the system are performed to prove the existence of chaos. Finally, the corresponding simulations are carried out on Matlab to illustrate the theoretical results.