Neural organization of the locomotive oscillator

Abstract

We study the relation of neural development, organization, and activity to behavior. We provide a model of the locomotive oscillator, a neural system supplying alternating stimulation to extensor and flexor muscles creating an oscillatory motion. We propose a protocol by which this neural system starting from unstructured, unconnected neural populations develops structure and function. The protocol is studied by both computer simulation and mathematical analysis. Our main results are 1. The locomotive oscillator self-organizes and maintains its organization, assuming certain properties of the neural populations. 2. Imperfections disturbing the functional adequacy of the neural populations may lead to the deterioration and disappearance of the oscillatory behavior. 3. The locomotive oscillator may fail to organize if the development is not staged in time.

Cortical memory dynamics

“…We achieve this by introducing matrix valued bounds, lm v and lm , so that 1 (Linsker 1986;Willner et al 1993) …”

Self-organization of an oscillatory neural system

“…The results of a computer simulation which shows this is provided in Willner et at (1993) where the relation between Hypothesis A and synaptic plasticity is also discussed. The projection process: For each of the five types we associate a constant 4~(0, 1).…”

“…Any deviation from the trajectory in Regions 1 and 2 will cause the trajectory to miss P. The trajectory will enter Regions 3 or 5, and terminate as in one of the two earlier cases. In our simulation [6] this perturbation is supplied by the random nature of the exogenous stimualtion. In fact, in the computer simulation, the trajectory passing through P has never been seen.…”

“…Our model which consists of four neural populations, is based on the half center description of S. Miller and P. D. Scott (1987). In our earlier work (Willner et al (1993)) a computer simulation demonstrating the development and self-organization of the neural circuitry of the locomotive oscillator is given. There, biological concepts and ethological implications of such a self-organizing system are discussed along with connections of that work with ideas of M. Edelman (1987Edelman ( , 1988, D. O.…”

“…We write(6) as follows specifying the post-synaptic neuron of type R to be in R e splitting the last sum into contributions from R e and R F.Since the magnitude of all neural activity is bounded by unity, fiR < La[, ~FR < [al and ~RR < Ibl (cf. (30)).Therefore, for e sufficiently small, F R~ will be less than the threshold O R. Thus, for e sufficiently small, R E does not fire when E = 0 in the previous cycle.…”