Nonlinear differential equations in B(H) motivated by learning models


We study a system of ordinary differential equations in B(H), the space of all bounded linear operators on a separable Hilbert space 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. © Springer Science+Business Media, LLC 2009.

Publication Title

Journal of Dynamics and Differential Equations