Nonlinear Dynamical Multi-Scale Model of Associative Memory

How can we get such reliable behavior from the mind when the brain is made up of such unreliable elements as neurons? We propose that the answer is related to the emergence of stable brain states and we offer a model that illustrates how such states could arise. We discuss a new ab initio nonlinear dynamical multi-scale model that will serve as the foundation for an associative memory. Scale 0 consists of spiking Hodgkin-Huxley (HH) neurons. Scale 1 consists of components that are made up of large populations of HH neurons whose topological structure evolves according to a Hebbian-plasticity rule based on synchronous firing. The component's state is captured by the variance of phase synchrony for the population. Many such components are sparsely connected to form a large network, whose state can be captured by the n-tuple consisting of the individual states of each member component. Scale 2 takes the state of the overall network and upon examining the particular interrelationships of each component (determining how the state of one component affects the state of others) is able to generate a class of trajectories that is multistationary and stable periodic. Such a class we consider a memory, the encoding of many such memories leads to the creation of a robust associative memory. The details of the different scales are examined.