Andrey Chernyshov

The phenomenon of “bifurcation memory”, which can be detected during the steering of river vessels, is considered by researchers with the questions of equilibrium point’s bifurcations. It was noticed that in some dynamic systems during saddle-node bifurcation, areas are formed on the phase plane (so-called “phase spot”), passing through which the phase velocity of the representative point decreases. A decrease in phase velocity (e. g. during the steering of river vessel) can cause navigation accidents during shallow waters navigation. In order to improve sailing safety, it is necessary to investigate topological features of phase spots under any possible environmental conditions and steering angle values. In this paper, we propose a new method that makes it easy to get information about the localization of regions with decreased phase velocity. We gained the results related to the topology of areas of different types of motion (accelerated or decelerated) of representative point. In addition, the paper presents the process of evolution of these regions, according to the change of steering angles, as well as before and after the bifurcation. The new method, offered in the article, is more accurate for determining the boundaries of the areas compared to the methods of Feigin and Chirkova. This will allow us to make more correct predictions of changes in the dynamics of the object. The practical implication of the suggested method is that by using it, we can get information about the location of areas with different types of motion of the representative point on the phase plane for different values of steering angle and environmental conditions. This information can be used in the control algorithm of the driving object, for example, in order to predict the decreasing of phase velocities.