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RESEARCH PRODUCT

Coexistence of periods in a bifurcation

V. Botella-solerJ A OteoJ. Ros

subject

Period-doubling bifurcationInfinite setGeneral MathematicsApplied MathematicsMathematical analysisFísicaGeneral Physics and AstronomyStatistical and Nonlinear PhysicsSaddle-node bifurcationBifurcation diagramNonlinear Sciences::Chaotic DynamicsTransition pointAttractorInfinite-period bifurcationBifurcationMathematics

description

Abstract A particular type of order-to-chaos transition mediated by an infinite set of coexisting neutrally stable limit cycles of different periods is studied in the Varley–Gradwell–Hassell population model. We prove by an algebraic method that this kind of transition can only happen for a particular bifurcation parameter value. Previous results on the structure of the attractor at the transition point are here simplified and extended.

yearjournalcountryeditionlanguage
2012-05-01Chaos, Solitons & Fractals
https://doi.org/10.1016/j.chaos.2011.11.008