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- W332225651 abstract "ABSTRACT The brain is indeed a highly hierarchical system in which a component net of one level functions as the building block of higher-level nets. It is necessary to develop a proper mathematical method and technique for elucidating each level. The present rather expository paper summarizes the author's recent endeavor of developing various mathematical techniques and obtaining characteristic features of nerve nets of the various levels. Following the Introduction (Section 1), Section 2 treats the dynamics of neuron pools, which are the elementary building blocks of neural systems. A simple neuron pool has monostable or bistable dynamics depending on the parameters of the pool. The dynamical properties of a neuron pool give rise to multistable, hysteretic, and oscillatory phenomena, which play an essential role in a higher-level system. In Section 3 we consider the dynamics of neural fields, which can be regarded as systems consisting of spatially distributed neuron pools having mutual connections. We present a mathematical method by which we analyze the dynamics of pattern formation in neural fields. Section 4 deals with the learning or self-organizing capabilities of neural systems. We search for a common neural mechanism which realizes high-level information processing, such as association and concept formation." @default.
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- W332225651 date "1977-01-01" @default.
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- W332225651 title "A Mathematical Approach to Neural Systems" @default.
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- W332225651 doi "https://doi.org/10.1016/b978-0-12-491850-4.50008-8" @default.
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