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Dynamics of a map with a power-law tail

2008/12/31 by V. Botella-Soler, V Botella-Soler, J A Oteo +3
Environmental Science · Medicine · Physics and Astronomy · #Bifurcation #Chaos control and synchronization #Chaotic #Dynamics (music) #Ecosystem dynamics and resilience #Limit (mathematics) #Mathematical and Theoretical Epidemiology and Ecology Models #Period-doubling bifurcation #Piecewise #Population #Saddle-node bifurcation #Type (biology) #nlin.CD

paper · pdf · doi:10.1088/1751-8113/42/38/385101

published as V Botella-Soler et al 2009 J. Phys. A: Math. Theor. 42 385101 (22pp) · 28 pages, 17 figures

openalex publication_date 2009/09/02 · arxiv created 2011/02/02 · arxiv updated 2015/03/13 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05

Abstract

We analyze a one-dimensional piecewise continuous discrete model proposed originally in studies on population ecology. The map is composed of a linear part and a power-law decreasing piece, and has three parameters. The system presents both regular and chaotic behavior. We study numerically and, in part, analytically different bifurcation structures. Particularly interesting is the description of the abrupt transition order-to-chaos mediated by an attractor made of an infinite number of limit cycles with only a finite number of different periods. It is shown that the power-law piece in the map is at the origin of this type of bifurcation. The system exhibits interior crises and crisis-induced intermittency.

Citations