Dynamical Analysis of the Incommensurate Fractional-Order Hopfield Neural Network System and Its Digital Circuit Realization

Abstract

Dynamical analysis of the incommensurate fractional-order neural network is a novel topic in the field of chaos research. This article investigates a Hopfield neural network (HNN) system in view of incommensurate fractional orders. Using the Adomian decomposition method (ADM) algorithm, the solution of the incommensurate fractional-order Hopfield neural network (FOHNN) system is solved. The equilibrium point of the system is discussed, and the dissipative characteristics are verified and discussed. By varying the order values of the proposed system, different dynamical behaviors of the incommensurate FOHNN system are explored and discussed via bifurcation diagrams, the Lyapunov exponent spectrum, complexity, etc. Finally, using the DSP platform to implement the system, the results are in good agreement with those of the simulation. The actual results indicate that the system shows many complex and interesting phenomena, such as attractor coexistence and an inversion property, with dynamic changes of the order of q0, q1, and q2. These phenomena provide important insights for simulating complex neural system states in pathological conditions and provide the theoretical basis for the later study of incommensurate fractional-order neural network systems.