On discrete pseudohyperbolic attractors of Lorenz type

Abstract

We study geometrical and dynamical properties of the so-called discrete Lorenz-like attractors, that can be observed in three-dimensional diffeomorphisms. We propose new phenomenological scenarios of their appearance in one parameter families of such maps. We pay especially our attention to such a scenario that can lead to period-2 Lorenz-like attractors. These attractors have very interesting dynamical properties and we show that their crises can lead, in turn, to the emergence of pseudohyperbolic discrete Lorenz shape attractors of new types. We also show examples of all these attractors in three-dimensional generalized Hénon maps.

Wild pseudohyperbolic attractor in a four-dimensional Lorenz system

“…More general universal bifurcation scenarios leading to discrete Lorenz-like attractors were proposed in[37]. Such scenarios are realized in three-dimensional Hénon-like maps[33,34,40] and in nonholonomic models of Celtic stone[35,38].…”