ssingh@watserv1.waterloo.edu ($anjay "lock-on" $ingh - Indy Studies) (01/16/90)
Here are the some references to chaos-theoretic descriptions of the brain.
They are from Neural and Brain Modelling. I also have the Fortran files
for the simulation programs contained therein. They are the correct ones.
Someone mentioned a few months ago about errors in the book. I hope
this proves useful to some of you, given the recent talk about chaos and
brains.
Chay, T.R. Abnormal discharges and chaos in a neuronal model system.
_Biological Cybernetics_. 50, 301-311
Abstract: Using the mathematical model of the pacemaker neuron formulated by
Chay, we have investigated the conditions in which a neuron can generate
chaotic signals in response to variation in temperature, ionic compositions,
chemicals, and the strength of the depolarizing current.
Choi, M.Y., and Huberman, B.A. Dynamic Behaviour of nonlinear networks.
_Phys. Rev. A_. 28, 1204-1206.
Abstract: We study the global dynamics of nonlinear networks made up of
synchronous threshold elements. By writing a master equation for the
system, we obtain an expression for the time dependence of its activity
as a function of parameter values. We show that with both excitatory
and inhibatory couplings, a network can display collective behaviour
which can be either multiple periodic or deterministic chaotic, a result
that appears to be quite general.
Grondin, R.O., et. al. Synchronous and Asynchronous Systems of Threshold
Elements. _Biological Cybernetics_. 49, 1-7.
Abstract: The role of synchronism in systems of threshold elements (such
as neural networks) is examined. Some important differences between
synchronous and asynchronous systems are outlined. In particular,
important restrictions on limit cycles are found in asynchronous systems
along with multi-frequency oscillations which do not appear in synchronous
systems. The possible role of deterministic chaos in these systems is
discussed.
Guevara, M.R., Glass, L., Mackey, M.C., Shrier, A. Chaos in Neurobiology.
_IEEE Transactions on Systems, Man, and Cybernetics_. 13, 790-798.
Abstract: Deterministic mathematical models can give rise to complex
aperiodic ("chaotic") dynamics in the abscence of stochastic fluctuations
("noise") in the variables or parameters of the model or in the inputs
to the system. We show that chaotic dynamics are expected in nonlinear
feedback systems possessing time delays such as are found in recurrent
inhibition and from the periodic forcing of neural oscillators. The
implications of the possible occurrence of chaotic dynamics for experimental
work and mathematical modelling of normal and abnormal function in
neurophysiology are mentioned.
Holden, A.V., Winlow, W., and Hayden, P.G. The Induction of Periodic
and Chaotic Activity in a Molluscan Neurone. _Biological Cybernetics_.
43, 169-173.
Abstract: During prolonged exposure to extracellular 4-aminopyridine (4AP)
the periodic activity of the somatic membrane of an identified molluscan
neurone passes from a repetitive regular discharge of >90 mV amplitude
action potentials, through double discharges to <50 mV amplitude
oscillations. Return to standard saline causes the growth of parabolic
amplitude-modulated oscillations that develop, through chaotic amplitude-
modulated oscillations, into regular oscillations. These effects are
interpreted in terms of the actions of 4AP on the dynamics of the membrane
excitation equations.
$anjay "lock-on" $ingh
ssingh@watserv1.waterloo.edu
"A modern-day warrior, mean mean stride, today's Tom Sawyer, mean mean pride."
--
$anjay "lock-on" $ingh
ssingh@watserv1.waterloo.edu
"A modern-day warrior, mean mean stride, today's Tom Sawyer, mean mean pride."