Dynamical stability of formation of cortical maps

A cortical map is a localized neural representation of the signals in the outer world. A rough map is formed under the guidance of genetic information at the initial stage of development, but it is modified and refined further by self­ organization. The persent paper gives a mathematical theory of formation of a cortical map by self-organization. The theory treats both dynamic of excitation patterns and dynamics of self-organization in a neural field. This not only explains the resolution and amplification properties of a cortical map, but elucidates the dynamical stability of such a map. This explains the emergence of a microcolumnar or mosaic structure in the cerebrum.

[1]  E. Caianiello.  Outline of a theory of thought-processes and thinking machines. , 1961, Journal of theoretical biology.

[2]  K. Pribram,et al.  Biology of memory , 1970 .

[3]  D. N. Spinelli.  OCCAM: A COMPUTER MODEL FOR A CONTENT ADDRESSABLE MEMORY IN THE CENTRAL NERVOUS SYSTEM , 1970 .

[4]  Shun-ichi Amari,et al.  Learning Patterns and Pattern Sequences by Self-Organizing Nets of Threshold Elements , 1972, IEEE Transactions on Computers.

[5]  Ludvík Prouza,et al.  On the weight matrices of linear difference equations , 1976, Kybernetika.

[6]  C. Malsburg,et al.  How patterned neural connections can be set up by self-organization , 1976, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[7]  S. Amari,et al.  A Mathematical Foundation for Statistical Neurodynamics , 1977 .

[8]  Roman Bek,et al.  Discourse on one way in which a quantum-mechanics language on the classical logical base can be built up , 1978, Kybernetika.

[9]  S. Amari,et al.  Existence and stability of local excitations in homogeneous neural fields , 1979, Journal of mathematical biology.

[10]  Shun-Ichi Amari,et al.  Topographic organization of nerve fields , 1979, Neuroscience Letters.

[11]  T. Kohonen.  Self-organized formation of topographically correct feature maps , 1982 .

[12]  M. Arbib,et al.  Systems Matching and Topographic Maps: The Branch-Arrow Model (BAM) , 1982 .

[13]  S. Amari,et al.  Competition and Cooperation in Neural Nets , 1982 .

[14]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[15]  Shun-ichi Amari,et al.  Field theory of self-organizing neural nets , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[16]  Shun-ichi Amari,et al.  Statistical neurodynamics of associative memory , 1988, Neural Networks.