期刊
CHAOS SOLITONS & FRACTALS
卷 31, 期 2, 页码 305-315出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2006.01.034
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资金
- ICREA Funding Source: Custom
In this paper we analyze delayed transition phenomena associated to extinction thresholds in a mean field model for hypercycles composed of three and four units, respectively. Hence, we extend a previous analysis carried out with the two-membered hypercycle [see Sardanyes J, Sole RV. Ghosts in the origins of life? Int J Bifurcation Chaos 2006;16(9), in press]. The models we analyze show that, after the tangent bifurcation, these hypercycles also leave a ghost in phase space. These ghosts, which actually conserve the dynamical properties of the coalesced coexistence fixed point, delay the flows before hypercycle extinction. In contrast with the two-component hypercycle, both ghosts show a plateau in the delay as phi -> 0, thus displacing the power-law dependence to higher values of 0, in which the scaling law is now given by tau similar to phi(beta), with beta = -1/3 (where T is the delay and 0 = e - c, the parametric distance above the extinction bifurcation point). These results suggest that the presence of the ghost is a general property of hypercycles. Such ghosts actually cause a memory effect which might increase hypercycle survival chances in fluctuating environments. (c) 2006 Elsevier Ltd. All rights reserved.
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