  We suggest a universal map capable to recover a behavior of a wide range of
dynamical systems given by ODEs. The map is built as an artificial neural
network whose weights encode a modeled system. We assume that ODEs are known
and prepare training datasets using the equations directly without computing
numerical time series. Parameter variations are taken into account in the
course of training so that the network model captures bifurcation scenarios of
the modeled system. Theoretical benefit from this approach is that the
universal model admits using common mathematical methods without needing to
develop a unique theory for each particular dynamical equations. Form the
practical point of view the developed method can be considered as an
alternative numerical method for solving dynamical ODEs suitable for running on
contemporary neural network specific hardware. We consider the Lorenz system,
the Roessler system and also Hindmarch-Rose neuron. For these three examples
the network model is created and its dynamics is compared with ordinary
numerical solutions. High similarity is observed for visual images of
attractors, power spectra, bifurcation diagrams and Lyapunov exponents.
