Dynamics study on the effect of memristive autapse distribution on Hopfield neural network

As the shortest feedback loop of the nervous system, autapse plays an important role in the mode conversion of neurodynamics. In particular, memristive autapses can not only facilitate the adjustment of the dynamical behavior but also enhance the complexity of the nervous system, in view of the fact that the dynamics of the Hopfield neural network has not been investigated and studied in detail from the perspective of memristive autapse. Based on the traditional Hopfield neural network, this paper uses a locally active memristor to replace the ordinary resistive autapse so as to construct a 2 n-dimensional memristive autaptic Hopfield neural network model. The boundedness of the model is proved by introducing the Lyapunov function and the stability of the equilibrium point is analyzed by deriving the Jacobian matrix. In addition, four scenarios are established on a small Hopfield neural network with three neurons, and the influence of the distribution of memristive autapses on the dynamics of this small Hopfield neural network is described by numerical simulation tools. Finally, the Hopfield neural network model in these four situations is designed and implemented on field-programmable gate array by using the fourth-order Runge-Kutta method, which effectively verifies the numerical simulation results.