Model of biological pattern recognition with spatially chaotic dynamics

-This article describes" computer simulation of the dynamics of a distributed model of the ol)actory system that is aimed at understanding the role of chaos in biological pattern recognition. The model is governed bv coupled nonlinear differential equations with many variables and parameters', which allow multiple highdimensional chaotic states'. An appropriate set c~[ the parameters is identified by computer experiments with the guidance of biological measurements, through which this" model of the olfactory system maintains a low dimensional global chaotic attractor with multiple ~" wings,'" The central part c~[ the attractor is its basal chaotic activity, which simulates the electroencephalographic (EEG) aetivi O' of the olfactory system under zero signal input (exhah~tion). It provides the system with a ready state so that it is unnecessary for the system to "wake up" front or return to a "'dormant" equilibrium state every time that an input is" given (by inhalation). Each of the wings may be either a near-limit cycle (a narrow band chaos') or a broad band chaos. The reproducible spatial pattern 0[ each near-limit cycle is" determined by a template made in the system. A novel input with no template activates the system to either a nonreproducible near-limit cycle wing or a broad band chaotic wing. Pattern recognition in the system may be considered as the transition from one wing to another, as demonstrated by the computer simulation. The time series of the manifestations" of the attractor are EEG-like waveforms with fractal dimensions that reflect which wing the system is placed in by input or lack of input. The computer simulation also shows that the adaptive behavior of the system is scaling invariant, and it is independent of the initial conditions at the transition ,f?om one wing to another. These properties" enable the system to classify an uninterrupted sequence Of stimtdi. Keywords--Chaos, Neural networks, Olfaction modeling, Pattern classification, Phase coherence, Scaling invariance, Serial recognition. I. I N T R O D U C T I O N The study of neural networks has opened a new direction in the investigation of novel computer design principles through understanding complex dynamics in biological brains. The marriage of nonlinear dynamics and neurobiology may be very helpful to the field of artifical intelligence by capturing the speed and power of brains during pattern recognition. Acknowledgments: Support from grants AFOSR-87-0317 and MH06686 from NIMH is gratefully acknowledged. The authors thank Harold Szu, physicist; Bill Baird, biophysicist; Barry Rhoades, physiologist; Morris Hirsch, mathematician: and Marjorie Honzik, psychologist, for their careful reading of the original manuscript and their valuable suggestions. The current revised version has benefited from helpful comments by one anonymous action editor and two anonymous referees. Requests tk~r reprints should be sent to Walter J. Freeman, Department of Molecular and Cell Biology, University of California, Berkeley. CA 94720. 1.1 Biological Phenomena Physiological experiments suggest that the main components of neural activity in olfactory systems are chaotic (Skarda & Freeman, 1987). It has been found that distributions of intervals between pulses in trains are typically Poisson; histograms of electroencephalographic (EEG) amplitudes are close to Gaussian curves; and spectra of brain waves are broad with low and variable peaks consistent with 1 / f noise (Freeman, 1975). Fractal dimensions are estimated to be low (Freeman, 1987, 1988). An equilibrium occurs only under deep anesthesia, in coma, or in areas of cortex that have been isolated from the rest of the brain. There is no evidence that pure limit cycle activity appears in olfactory systems, although at times the activities of neurons may come close to a limit cycle. Our physiological experiments tell us: (a) The EEG manifests a particular kind of Chaos that is spatially coherent across the cortex when sampled with an array of electrodes; (b) the adaptive