On Explicitly Solvable Gradient Systems of Moser]Karmarkar Type

A generalization and a classification of explicitly solvable gradient systems which appear in linear programming and neurodynamics are studied, It is shown that nonlinear dynamical systems of Moser]Karmarkar type generically take both a Lax representation and a gradient form. A related optimization problem on a simplex is discussed. An integration procedure and a complete description of the invariant manifolds and the phase portrait of the dynamical systems of Moser]Karmarkar type are also investigated.