  The review presents a parameter switching algorithm and his applications
which allows numerical approximation of any attractor of a class of
continuous-time dynamical systems depending linearly on a real parameter. The
considered classes of systems are modeled by a general initial value problem
embedding dynamical systems which are continuous and discontinuous with respect
to the state variable, and of integer and fractional order. The numerous
results, presented in several papers, are systematized here on four
representative known examples representing the four classes. The analytical
proof of the algorithm convergence for the systems belonging to the continuous
class is briefly presented, while for the other categories of systems the
convergence is numerically verified via computational tools. The utilized
numerical tools necessary to apply the algorithm are contained in five
appendices.
