Stochastic neurodynamics. (English) Zbl 0686.92009
Summary: Stochastic dynamics of relative membrane potential in the neural network is investigated. It is called stochastic neurodynamics. The least action principle for stochastic neurodynamics is assumed, and used to derive the fundamental equation. It is called a neural wave equation. A solution of the neural wave equation is called a neural wave function and describes stochastic neurodynamics completely. Linear superposition of neural wave functions provides us with a mathematical model of associative memory process.
As a simple application of stochastic neurodynamics, a mathematical representation of static neurodynamics in terms of equilibrium statistical mechanics of spin systems is derived.
As a simple application of stochastic neurodynamics, a mathematical representation of static neurodynamics in terms of equilibrium statistical mechanics of spin systems is derived.
MSC:
92Cxx | Physiological, cellular and medical topics |
60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
82B99 | Equilibrium statistical mechanics |
Keywords:
neural holography; Stochastic dynamics of relative membrane potential; neural network; stochastic neurodynamics; least action principle; neural wave equation; neural wave function; Linear superposition; associative memory process; static neurodynamics; equilibrium statistical mechanics of spin systemsReferences:
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