There is short description of problem state on nonlinear dynamics in this paper. Information about some contemporary journals and recent Conferences on this subject is given. Information about 5-th International Conference on Nonlinear Dynamics which was holding in National Technical University "Kharkov Polytechnic Institute" in September 2016 and impression about it are presented. The questions that were discussed at this conference are in domain of our special interests. Dynamic behaviour of non-smooth systems with discontinuous right-hand side is the main contemporary question. Many new phenomena unique to non-smooth systems are observed under variation of system parameters. Such nonlinear problems are arising in many different domains of science and engineering, for example in mechanics, physics, radio technique, biology, chemistry, economics, ecology, sociology, and so on. The investigations of nonlinear dynamics problems in general and very complex phenomenon of chaos in particular were begun quite recently і only in the end of 20-th century. Vibroimpact system is one example of nonlinear systems. It is strongly nonlinear non-smooth discontinuous system because the set of its motion differential equations contains the discontinuous right-hand side. The bifurcations of different kind occur in vibroimpact system under system parameter variation. The bifurcation analysis execution and the bifurcation diagrams building allow to find and to distinguish the safe, explosive, and dangerous bifurcations in dissipative dynamical systems. In systems with discontinuous right-hand side the discontinuous bifurcation can occur when system parameter is varying. Discontinuous bifurcations that occur in non-smooth vibroimpact systems are dangerous ones. At 5th International Conference on nonlinear dynamics (ND-KhPI2016, Kharkiv, Ukraine) we presented the talk entitled "Discontinuous Bifurcations under 2-DOF Vibroimpact System Moving". We offered numerical analysis by parameter continuation method of vibroimpact system dynamic behaviour. We simulated impact by nonlinear contact force according to Hertzіs contact law. In such way we have obtained the possibility to find the motion law along the whole timebase including the impact phase, to determine the impact duration and to find the contact impact forces. We have found dangerous discontinuous bifurcations and have observed phenomena unique for non-smooth systems with discontinuous right-hand side. We have observed the fold dangerous bifurcation in our vibroimpact system.

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