6533b873fe1ef96bd12d4cda
RESEARCH PRODUCT
Dynamics of a map with a power-law tail
V. Botella-solerJ RosJ A Oteosubject
Statistics and ProbabilityMathematical analysisChaoticFOS: Physical sciencesGeneral Physics and AstronomyFísicaStatistical and Nonlinear PhysicsNonlinear Sciences - Chaotic DynamicsPower lawlaw.inventionNonlinear Sciences::Chaotic DynamicslawModeling and SimulationIntermittencyAttractorPiecewiseLimit (mathematics)Chaotic Dynamics (nlin.CD)Finite setMathematical PhysicsBifurcationMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-12-24 |