Chaotic Dynamics in a Fractional-Order Hopfield Neural Network and its Stabilization via an Adaptive Model-Free Control Method

The present study introduces a kind of fractional-order Hopfield neural network (FOHNN)‎, ‎and its complex dynamic behavior is investigated through chaos analyses‎. ‎With the use of phase space analysis and bifurcation diagrams and maximal Lyapunov exponent (MLE) it is demonstrated that for the values of 0.87 < α < 1‎, as the fractional-order (FO)‎, ‎the dynamical behavior of the mentioned FOHNN is chaotic‎. ‎Then‎, ‎the bounded trait of chaotic systems is utilized to derive an adaptive model-free control technique to suppress of complex dynamics of the FOHNN‎. ‎Furthermore‎, ‎according to the matrix analysis theorem of non-integer-order systems and the adaptive model-free control methodology‎, ‎analytical consequences of the designed controller are evidenced‎. ‎Eventually‎, ‎two examples are reported to illustrate the applicability of the mentioned model-free control method.