0 A Dynamical System with Two Strange Attractors

A six-dimensional Rössler-Lorenz hybrid has two coexistent attractors. Both, either or neither may be strange. Introduction. The Rössler [1] and Lorenz [2] equations are textbook examples of chaotic dynamical systems. Each is three-dimensional, continuoustime, smooth and autonomous, with a single strange attractor for certain parameter values. This paper draws attention to a six-dimensional hybrid with two coexistent attractors, one or both of which may be strange. The attractors evidently stem from the constituent Rössler and Lorenz systems, but each requires and occupies the larger phase space. The new system may well have potential for physical modelling, but its discovery is the result of curiosity. Construction. Start with the Lorenz equations [2] ẋ = σ(y − x) ẏ = (r − z)x− y (1) ż = xy − βz in a chaotic regime with σ = 10, r = 28, β = 8 3 . (2) ∗[email protected]