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Zero–Hopf bifurcation in a hyperchaotic Lorenz system

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Abstract

We characterize the zero–Hopf bifurcation at the singular points of a parameter codimension four hyperchaotic Lorenz system. Using averaging theory, we find sufficient conditions so that at the bifurcation points two periodic solutions emerge and describe the stability of these orbits.

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Acknowledgements

The second author is partially supported by a MINECO/ FEDER grant number MTM2008-03437, by an AGAUR grant number 2009-SGR-410, by ICREA Academia and by FP7-PEOPLE-2012-IRSES 316338 and 318999. The first and third authors were partially supported by a NSERC Discovery Grant.

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Authors and Affiliations

  1. Department of Mathematics, Wilfrid Laurier University, Waterloo, N2L 3C5, Ontario, Canada

    Lorena Cid-Montiel & Cristina Stoica

  2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Catalonia, Spain

    Jaume Llibre

Authors
  1. Lorena Cid-Montiel
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  2. Jaume Llibre
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  3. Cristina Stoica
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Correspondence to Cristina Stoica.

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Cid-Montiel, L., Llibre, J. & Stoica, C. Zero–Hopf bifurcation in a hyperchaotic Lorenz system. Nonlinear Dyn 75, 561–566 (2014). https://doi.org/10.1007/s11071-013-1085-3

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  • DOI: https://doi.org/10.1007/s11071-013-1085-3

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