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Coexistence of periods in a bifurcation

Author

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  • Botella-Soler, V.
  • Oteo, J.A.
  • Ros, J.

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.

Suggested Citation

  • Botella-Soler, V. & Oteo, J.A. & Ros, J., 2012. "Coexistence of periods in a bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 681-686.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:5:p:681-686
    DOI: 10.1016/j.chaos.2011.11.008
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    References listed on IDEAS

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    1. Kiminori Matsuyama, 1999. "Growing Through Cycles," Econometrica, Econometric Society, vol. 67(2), pages 335-348, March.
    2. Matsuyama, Kiminori, 2001. "Growing through Cycles in an Infinitely Lived Agent Economy," Journal of Economic Theory, Elsevier, vol. 100(2), pages 220-234, October.
    3. Gardini, Laura & Sushko, Iryna & Naimzada, Ahmad K., 2008. "Growing through chaotic intervals," Journal of Economic Theory, Elsevier, vol. 143(1), pages 541-557, November.
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