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Nonlinear Differential Equations in \({\mathcal{B}(\mathcal{H})}\) Motivated by Learning Models

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Abstract

We study a system of ordinary differential equations in \({\mathcal{B}(\mathcal{H})}\) , the space of all bounded linear operators on a separable Hilbert space \({\mathcal{H}}\) . The system considered is a natural generalization of the Oja–Cox–Adams learning models. We establish the local existence of solutions and solve explicitly the system for a class of initial conditions. For such cases, we also characterize the asymptotic behavior of solutions.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, 38152, USA

    Fernanda Botelho & James E. Jamison

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  1. Fernanda Botelho
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  2. James E. Jamison
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Correspondence to Fernanda Botelho.

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Botelho, F., Jamison, J.E. Nonlinear Differential Equations in \({\mathcal{B}(\mathcal{H})}\) Motivated by Learning Models. J Dyn Diff Equat 21, 595–606 (2009). https://doi.org/10.1007/s10884-009-9148-3

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  • DOI: https://doi.org/10.1007/s10884-009-9148-3

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