[Comp-neuro] "Middle layer" coupled " neuron" program

ajmandell ajmandell at charter.net
Sat Sep 27 18:50:04 CEST 2008

To all, 

There's been some interest expressed in our coupled neuron, "MRM" map, some studies
of which were  published  in Physica D in 1989. It might be fun for others to explore its behavior since
most of its potential phenomenology has remained unexplored unreported) 

You can find it at www.cieloinstitute.org where you can use the coupled logistics
button and find the zipped downloadable program and a data file. 
The  data and graphics can be saved for analyses.

It runs on most common platforms. The published paper is also available at the site. 
The  combined one and two dimensional dynamical system models the output of coupled neurons.
The output of one modulates the parameter of the other. 
In  its rather interesting  two dimensional, quasi-symmetrical parameter space (illustrated in  the paper )                                                                                                
moving along the diagonal generates most if not all known one dimensional dynamics. Off diagonal exploration 
yields all or most if not all known in two dimensions (Hopf, tangent, quasi-periodic, period adding etc  bifurcations, 
Arnold's  tongues in a dissipative system, etc.  The output of the transitional parameter space  between 
one and two dimensions is interesting and complex (and relatively unexplored).  With some patience, it can be very rich.
The hierarchical  self similarity in some of the phase space objects is striking amd reminiscent of the "fractional scaling" reported
in some brain data.   

The system is operated by four convenient parameter "handles" and programmed in very close
to machine language so that things  run relatively quickly. 



Arnold J. Mandell, M.D.
Cielo Institute, Asheville, NC
ajmandell at charter.net
Clinical Professor of Psychiatry and Human Behavior, Emory University,
Adjunct Professor of Mathematical Sciences, FAU, Boca Raton, FL
Founding Chairman and Professor Emeritus of Psychiatry (Neuroscience,
Pharmacology, Mathematics) UCSD, La Jolla, CA
MacArthur Prize Fellow Laureate in Theoretical Neuroscience
Humboldt Prize Fellow Laureate in Dynamical Systems (Bremen University). 

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