Wild spiral attractors of Turaev-Shilnikov type in four-dimensional flows

The main goal of this work is to study various methods, analytical and numerical, that analyze the conditions for the destruction of a pseudo-hyperbolic attractor using the example of the Turaev-Shilnikov attractor. These methods can help to study the conditions under which a pseudo-hyperbolic attractor, if any, is destroyed, or to confirm that such an attractor exists in the system. As an example, we will consider a new system in which the Turaev-Shilnikov pseudo-hyperbolic attractor can exist (here we have in mind the conditions imposed on the equilibrium states, since in the Turaev-Shilnikov geometric model there are three equilibrium states and all three are saddle foci). In this work, a series of numerical experiments will be performed to determine the region of a pseudo-hyperbolic attractor in the system under study.