Eur. Phys. J. D 19, 119-124 (2002)
https://doi.org/10.1140/epjd/e20020063

A quasi-crisis in a quasi-dissipative system

¹ Institute of Plasma Physics, Chinese Academy of Sciences, P.O. Box 1126, Hefei 230031, P.R. China
² Complexity Science Center of Yangzhou University, Yangzhou 225002, P.R. China
³ CCAST (World Laboratory), P.O. Box 8730, Beijing 100080, P.R. China

Corresponding author: ^a drhe@mail.yzu.edu.cn

Received: 29 May 2001
Revised: 6 November 2001
Published online: 15 April 2002

Abstract

A system concatenated by two area-preserving maps may be addressed as “quasi-dissipative", since such a system can display dissipative behaviors. This is due to noninvertibility induced by discontinuity in the system function. In such a system, the image set of the discontinuous border forms a chaotic quasi-attractor. At a critical control parameter value the quasi-attractor suddenly vanishes. The chaotic iterations escape, via a leaking hole, to an emergent period-8 elliptic island. The hole is the intersection of the chaotic quasi-attractor and the period-8 island. The chaotic quasi-attractor thus changes to chaotic quasi-transients. The scaling behavior that drives the quasi-crisis has been investigated numerically.