Hysteresis is a unique type of dynamic, which contains an important propert
y, rate-independent memory. In addition to other memory-related studies suc
h as time delay neural networks, recurrent networks, and reinforcement lear
ning, rate-independent memory deserves further attention owing to its poten
tial applications. In this work, we attempt to define hysteretic memory (ra
te-independent memory) and examine whether or not it could be modeled in ne
ural networks. Our analysis results demonstrate that other memory-related m
echanisms are not hysteresis systems. A novel neural cell, referred to here
in as the propulsive neural unit, is then proposed. The proposed cell is ba
sed on a notion related the submemory pool, which accumulates the stimulus
and ultimately assists neural networks to achieve model hysteresis. In addi
tion to training by backpropagation, a combination of such cells can simula
te given hysteresis trajectories.