Heterogeneous Hopfield neural network with analog implementation

The activation function plays a crucial role as a nonlinear factor in the Hopfield neural network. However, limited attention has been given to studying heterogeneous activation functions. In this study, we present a three-neuron heterogeneous Hopfield neural network incorporating two distinct activation functions, namely hyperbolic tangent function and sine function. The kinetics of the heterogeneous neural network is investigated theoretically and numerically, and the kinetic effect of the sine activation function is revealed thereby. The findings demonstrate the presence of intricate kinetics, including chaos, period, stable point, and coexisting attractors, and the enlargement of chaotic kinetics distribution on the parameter plane by sine activation function within the heterogeneous neural network. Notably, an analog circuit is designed on a hardware level to simplify the implementation of the heterogeneous Hopfield neural network and experimental measurements provide strong validation for the numerical findings.