Merger of a Hénon-like attractor with a Hénon-like repeller in a model of vortex dynamics.

Abstract

We study the phenomenon of a collision of a Hénon-like attractor with a Hénon-like repeller leading to the emergence of mixed dynamics in the model describing the motion of two point vortices in a shear flow perturbed by an acoustic wave. The mixed dynamics is a recently discovered type of chaotic behavior for which a chaotic attractor of the system intersects with a chaotic repeller. In all known systems with mixed dynamics, the difference between the numerically obtained attractor and repeller is small. Unlike these systems, the model under consideration demonstrates another type of mixed dynamics that we call "strongly dissipative." In this case, a strange attractor and a strange repeller have a nonempty intersection but are very different from each other, and this difference does not appear to decrease with increasing computation time.