One of the most fundamental problems in multidi-mensional chaos theory is the study of strange attractors which are robustly chaotic (i.e., they remain chaotic after small perturbations of the system). It was hypothesized in [1] that the robustness of chaoticity is equivalent to the pseudohyperbolicity of the attractor. Pseudohyperbolicity is a generalization of hyperbolicity. The main characteristic property of a pseudohyperbolic attractor is that each of its orbits has a positive maximal Lyapunov exponent. In addition, this property must be preserved under small perturbations. The foundations of the theory of pseudohyperbolic attractors were laid by Turaev and Shilnikov, who showed that the class of pseudohyperbolic attractors, besides the classical Lorenz and hyperbolic attractors, also includes wild attractors which contain orbits with a homoclinic tangency.
In this talk, using the pseudohyperbolicity notion, we will explain how to check whether the attractor is robustly chaotic or not. We will describe the corresponding numerical methods and apply them for the study of networks of coupled phase oscillators.

This work was supported by the project Mirror Laboratories at HSE University.

References
1. Gonchenko S., Kazakov A. and Turaev D., 2021. Wild pseudohyperbolic attractor in a four-dimensional Lorenz system. Nonlinearity, 34(4), p.2018.