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.
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Wang, X.M., Wang, Y.M., Zhang, K. et al. A quasi-crisis in a quasi-dissipative system. Eur. Phys. J. D. 19, 119–124 (2002). https://doi.org/10.1140/epjd/e20020063
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DOI: https://doi.org/10.1140/epjd/e20020063