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Functions of Ubiquitous Chaos
By looking at the four states of the olfactory bulb, it seems clear that the most natural of these states for the bulb to be in is that of chaos. It comes in the form of a low amplitude background activity during an unmotivated waking state and as a higher amplitude noise during the exhalation state. Furthermore, the exhalation process always degrades the oscillatory inhalation attractor back into the chaotic attractor. Thus we are left with two non-chaotic states of the bulb which we can surely say are atypical: deep anesthesia and seizure.
This profound concept, chaos as the natural olfactory bulb state, poses a deep question: What function could natural, ubiquitous chaos serve?

The question of a function for ubiquitous chaos opens up a wide scope of interpretation. Particularly of interest are those ideas put forth by Walter J. Freeman, Walter J. Freeman Neurophysiology Lab, University of California at Berkeley and those of Chris King , Senior Lecturer, Department of Mathematics, University of Auckland, New Zealand.

The four possible functions for ubiquitous chaotic activity theorized by Freeman: [1]

    A rapid method of memory access.
    A chaotic attractor "provides rapid and ubiassed access to all of the collection of latent attractors". Furthermore, the descent from chaos into an oscillatory burst attractor is accomplished in a seemingly unpredictable way depending on the olfactory bulb environment during inhalation. "The low dimensional 'noise' is 'turned off' at the moment of bifurcation to a [limit cycle] attractor, and it is 'turned on' again on reverse bifurcation as the [limit cycle] vanishes."
    The following questions arose regarding the idea of Chaotic Access Memory (CAM): (1) How easy is it for a particular chaotic attractor to degrade into a given limit cycle? Is there some sort of measure of how 'distant' two attractors are from each other, specifically in terms of how one can turn into the other for a given system? (2) How much time or how many cycles are needed for the brain to recognize a given periodic orbit? This could illuminate some sort of lower limit to the speed at which a scent can be identified. (3) What method is employed to allow transition from chaotic attractor into limit cycle and vice versa?

    The 'novel stimulus' flag.
    "It appears that a novel odor interferes with the background and leads to failure of convergence to any patterned attractor." The olfactory bulb's following chaotic output (from inhalation) then serves as a signal that an unidentified odor has been detected. Furthermore, the classification of this new odor occurs "as rapidly reliably as the classification of any known odor, without requiring an exhaustive search through an ensemble of classifiable patterns that is stored in the brain." This novel classification system seems to be directly linked with the CAM system discussed above.

    Neuronal excercise.
    The chaotic attractor serves to stimulate a variety of neurons in a way that is neither over-stimulating nor neglecting. This emerges from the attractor's topology being spread out in an unstructured yet continous manner over the space-time of a large number of neurons. It is precisely this unstructured nature that serves to appropriately excercise the neurons contained within the attractor's boundary.

    A drive for new nerve cell connectivity.
    "[T]he chaotic activity evoked by a novel odor provides unstructured activity that can drive the formation of a new nerve cell assembly by strengthening of synapses between pairs of neurons having highly correlated activity... . Chaos allows the system to escape from its established repertoire of responses in order to add a new response to a novel stimulus under reinforcement."
    It is apparent that this function for chaos stems out of both the "neuronal excercise" and CAM concepts discussed above.

Basic outline of some of the proposed roles for chaotic processes in brain function, based on Chris King's list of suggested roles: [2]

    Chaotic Access
    They provide a stable, yet perpetually poised state which is equally ready for transition into each of the other possible stable states. Transition between chaotic and periodic states we might call transition across the meridian of complexity. "they allow unbiased access to stable states, provide escape from stable states under unfamiliar stimulus and the ability to create new states."

    "They provide a basis for the development of symbols as the stable attractors of the dynamics form a more fundamental dynamical continuum. Thus while the models of artificial intelligence cannot fully represent chaos, dynamics may be able to represent symbol creation and manipulation."

    Self-organizing Stability Structures
    "They provide a natural spatially-global basis for developing self-organization through stability structures, similar to the role of protein tertiary structure in complementing the data storage of the genetic code. Physical systems such as turbulent fluids display formation of fractal dissipative bifurcations, which are a rich source of new structure. Chaotic variation may thus be a central route for developing new structures in the brain."

    Local Minima Escaping
    "The need for random processes such as annealing, provides a basis for chaotic fluctuations to escape local minima in constrained optimizations."

    Data Compression
    "They may enable a very efficient form of data compression in memory in which the complexity of a given CNS state is reduced to the topological form of key attractors. A similar role has been proposed for the filtering action of integrative attention."

    "They provide for a potentially indeterminate brain consistent with the roles of consciousness and free-will."

[1] W. J. Freeman
Simulation of Chaotic EEG Patterns witha Dynamic Model of the Olfactory System
Biological Cybernetics. vol.56, pp.139-150, p.147. 1987.
[2] Chris King
Fractal and Chaotic Dynamics in Nervous Systems
Progress in Neurobiology. vol.36, pp.279-308. 1991

Last modified: Tue Jan 4 09:24:41 PST 2000