Taming chaos: stabilization of aperiodic attractors by noise [olfactory system model]

A model named “KIII” of the olfactory system contains 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 EEGs, 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 (~10^-16). 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