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“Theoretical Observations About the Hysteretic Hopfield Neural Network”
by Sunil Bharitkar and Jerry M. Mendel
June 1998
Several neuron activation functions have been proposed (e.g., linear, binary, sigmoid) for recurrent and multilayer Artificial Neural Networks. In this report we present a hysteretic neuron activation function for optimization and learning. We include this neuron within the framework of the Hopfield network to form the Hysteretic Hopfield Neural Network (HHNN). We then propose a dynamical equation, and an energy equation for this model using the well known Cohen-Grossberg theorem. Finally, these equations are used to prove Lyapunov stability of the HHNN.