  Utilization of multiple trajectories of a dynamical system model provides us
with several benefits in approximation of time series. For short term
predictions a high accuracy can be achieved via switches to new trajectory at
any time. Different long term trends (tendency to different stationary points)
of the phase portrait characterize various scenarios of the process realization
influenced by externalities. The dynamical system's phase portrait analysis
helps to see if the equations properly describe the reality. We also extend the
dynamical systems approach (discussed in \cite{R5}) to the dynamical systems
with external control.
  We illustrate these ideas with the help of new examples of the rental
properties HOMES.mil platform data. We also compare the qualitative properties
of HOMES.mil and Wikipedia.org platforms' phase portraits and the corresponding
differences of the two platforms' users. In our last example with COVID-19 data
we discuss the high accuracy of the short term prediction of confirmed
infection cases, recovery cases and death cases in various countries.
