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Viewing a class of neurodynamics on parameter space

  • Jianfeng Feng
  • David Brown
Complex Systems Dynamics
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1240)

Abstract

Nearly all models in neural networks start from the assumption that the input-output characteristic is a sigmoidal function. On parameter space we present a systematic and feasible method for analyzing the whole spectrum of attractors-all saturated, all-but-one saturated, all-but-two saturated, etc. — of a neurodynamical system with a saturated sigmoidal function as its input-output characteristic. We present an argument which claims, under a mild condition, that only all saturated or all-but-one saturated attractors are observable for the neurodynamics. For any given all saturated configuration ξ (all-but-one saturated configuration η) the paper shows how to construct an exact parameter region R(ξ) (¯R(η)) such that if and only if the parameters fall within R(ξ) (¯R(η)), then ξ (η) is an attractor (a fixed point) of the dynamics. The parameter region for an all saturated fixed point attractor is independent of the specific choice of a saturated sigmoidal function, whereas for an all-but-one saturated fixed point it is sensitive to the input-output characteristic.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Jianfeng Feng
    • 1
  • David Brown
    • 1
  1. 1.Biomathematics LaboratoryThe Babraham InstituteCambridgeUK

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