Towards a continuous dynamic model of the Hopfield theory on neuronal
interaction and memory storage
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Abstract
The purpose of this work is to study the Hopfield model for neuronal
interaction and memory storage, in particular the convergence to the stored
patterns. Since the hypothesis of symmetric synapses is not true for the
brain, we will study how we can extend it to the case of asymmetric
synapses using a probabilistic approach. We then focus on the description
of another feature of the memory process and brain: oscillations. Using the
Kuramoto model we will be able to describe them completely, gaining the
presence of synchronization between neurons. Our aim is therefore to
understand how and why neurons can be seen as oscillators and to establish
a strong link between this model and the Hopfield approach