Neurodynamics and nonlinear integrable systems of Lax type

DOI10.1007/BF03167210zbMath0822.92003OpenAlexW2045520233MaRDI QIDQ1325128

Yoshimasa Nakamura

Publication date: 24 May 1994

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03167210

zbMATH Keywords

gradient systemHopfield modelneurodynamicsLax pair representationnonlinear integrable systemsLax type equationconstrained harmonic motionaveraged learning equationfinite nonperiodic Toda lattice equationstochastic learning equation of Hebb type

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Neural networks for/in biological studies, artificial life and related topics (92B20) Applications of stochastic analysis (to PDEs, etc.) (60H30) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

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On explicit solvable gradient systems of Moser-Karmarkar type, Geodesic flows of \(\alpha \)-connections for statistical transformation models on a compact Lie group, Jacobi algorithm for symmetric eigenvalue problem and integrable gradient system of Lax form, On an integrable discretization of the Rayleigh quotient gradient system and the power method with a shift, Information Geometry and Integrable Hamiltonian Systems, Information geometry and Hamiltonian systems on Lie groups, Koszul information geometry, Liouville-Mineur integrable systems and Moser isospectral deformation method for Hermitian positive-definite matrices

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