UC Berkeley

A model named “KIII” of the olfactory system con-

tains an array of 64 coupled oscillators simulating the olfactory

bulb (OB), with negative and positive feedback through low-pass

filter lines from single oscillators simulating the anterior olfactory

nucleus (AON) and prepyriform cortex (PC). It is implemented

in C to run on Macintosh, IBM, or UNIX platforms. The output

can be set by parameter optimization to point, limit cycle,

quasi-periodic, or aperiodic (presumably chaotic) attractors. The

first three classes of solutions are stable under variations of

parameters and perturbations by input, but they are biologically

unrealistic. Chaotic solutions simulate the properties of time-

dependent densities of olfactory action potentials and EEG’s,

but they transit into the basins of point, limit cycle, or quasi-

periodic attractors after only a few seconds of simulated run time.

Despite use of double precision arithmetic giving 64-bit words, the

KIII model is exquisitely sensitive to changes in the terminal bit

of parameters and inputs. The global stability decreases as the

number of coupled oscillators in the OB is increased, indicating

that attractor crowding reduces the size of basins in the model to

???the size of the digitizing step (??? ). Chaotic solutions having

biological verisimilitude are robustly stabilized by introducing low-level, additive noise from a random number generator at two biologically determined points: rectified, spatially incoherent noise on each receptor input line, and spatially coherent noise to the AON, a global control point receiving centrifugal inputs from various parts of the forebrain. Methods are presented for evaluating global stability in the high dimensional system from measurements of multiple chaotic outputs. Ranges of stability are shown for variations of connection weights (gains) in the KIII model. The system is devised for pattern classification.