On Lorenz-type attractors in a six-dimensional generalization of the Lorenz model

The topic of the paper — Lorenz-type attractors in multidimensional systems. We consider a six-dimensional model that describes convection in a layer of liquid, taking into account impurities in the atmosphere and liquid, as well as the rotation of the Earth. The main purpose of the work is to study bifurcations in the corresponding system and describe scenarios for the emergence of chaotic attractors of various types. Results. It is shown that in the system under consideration, both a classical Lorenz attractor (the theory of which was developed in the works of Afraimovich–Bykov–Shilnikov) and an attractor of a new type, visually similar to the Lorenz attractor, but containing a symmetric pair of equilibrium states, can arise. It has been established that the Lorenz attractor in this system is born as a result of the classical scenario proposed by L. P. Shilnikov. We propose a new scenario for the emergence of an attractor of the second type via bifurcations inside the Lorenz attractor. In the paper we also discuss homoclinic and heteroclinic bifurcations that inevitably arise inside the found attractors, as well as their possible pseudohyperbolicity.  

chaotic attractor, pseudohyperbolicity, Lorenz attractor, Lyapunov exponents, homoclinic bifurcations, heteroclinic bifurcations