ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Perturbation of Heteroclinic Cycles of the Lorenz Type


V. E. Tchernyshev

St.Petersburg State University,
Chair of Differential Equations,
Bibliotechnaya sq., 2, 198904, St.Petersburg, Russia


The objective of this paper is to prove that there exists a small smooth perturbation of a three-dimensional system of ordinary differential equations with heteroclinic cycle of the Lorenz type such that in a neighbourhood of the cycle there is a chaotic locally maximal invariant set of the perturbed system. This chaotic set does not contain limit sets of the cycle.

Full text (pdf)