On discrete Lorenz-like attractors
С. В. Гонченко, A. S. Gonchenko, Alexey Kazakov, E. A. Samylina
Abstract
We study geometrical and dynamical properties of the so-called discrete Lorenz-like attractors. We show that such robustly chaotic (pseudohyperbolic) attractors can appear as a result of universal bifurcation scenarios, for which we give a phenomenological description and demonstrate certain examples of their implementation in one-parameter families of three-dimensional Hénon-like maps. We pay special attention to such scenarios 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 discrete Lorenz shape attractors of new types.
Topics & Concepts
AttractorLorenz systemChaoticBifurcationMathematicsStatistical physicsRössler attractorDynamical systems theoryApplied mathematicsComputer scienceMathematical analysisPhysicsNonlinear systemArtificial intelligenceQuantum mechanicsChaos control and synchronizationMathematical Dynamics and FractalsNonlinear Dynamics and Pattern Formation