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Existence and stability of local excitations in homogeneous neural fields (1979)

Kishimoto, K. ; Amari, S.

Springer

Journal of mathematical biology 7 (1979), S. 303-318

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ISSN: 1432-1416

Keywords: Neural field ; Waveform stability ; Lateral inhibition ; Dynamics of pattern formation ; Perron-Frobenius theorem

Source: Springer Online Journal Archives 1860-2000

Topics: Biology , Mathematics

Notes: Summary Dynamics of excitation patterns is studied in one-dimensional homogeneous lateral-inhibition type neural fields. The existence of a local excitation pattern solution as well as its waveform stability is proved by the use of the Schauder fixed-point theorem and a generalized version of the Perron-Frobenius theorem of positive matrices to the function space. The dynamics of the field is in general multi-stable so that the field can keep short-term memory.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00275151

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