  Algorithms of control of differential equations solutions are under
investigation in the article. Idealized and real modifications of the
algorithms are distinguished. An equation, which can be the base equation for
investigation of the idealized algorithms properties, is constructed. The
difference appearing for real systems and real algorithms is for separate
investigation. This difference tends to zero under tending to zero of the time
step of control. If the systems of equations satisfy or almost satisfy some
properties for which the algorithms are intended, then the results are similar
numerically as well. One of the algorithms demonstrates high reliability.
Another one is of more complex properties. Bifurcations, periodic solutions and
strange attractors are possible in both algorithms in addition to stable steady
states.
