  In this paper we study analytically a parameter switching (PS) algorithm
applied to a class of systems of ODE, depending on a single real parameter. The
algorithm allows the numerical approximation of any solution of the underlying
system by simple periodical switches of the control parameter. Near a general
approach of the convergence of the PS algorithm, some dissipative properties
are investigated and the dynamical behavior of solutions is investigated with
the Lyapunov function method. A numerical example is presented
