Finding Periodic Orbits in the Hindmarsh-Rose Neuron Model

  • M. Angeles MartínezEmail author
  • Roberto Barrio
  • Sergio Serrano
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 54)


In this work we apply a modified search method based on the stability transformation method, combined with the Newton method, to the classical neuronal model proposed by Hindmarsh and Rose in 1984. We have selected two values of parameter b corresponding to chaotic-bursting behavior (b = 2.69 and b = 3.05). For these values we have studied the changes of the chaotic attractors by obtaining the complete set of unstable periodic orbits up to multiplicity four. For b = 2.69 we have found 1, 1, 2 and 3 POs of multiplicity one to four, respectively, and for b = 3.05 we have found 1, 1, 0, 1 POs of multiplicity one to four, and thus giving a different chaotic attractor.


Periodic Orbit Initial Point Newton Method Chaotic Attractor Stable Manifold 
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This work is supported by Spanish Research project AYA2008-05572 (to M.A.M.) and by the Spanish Research project MTM2012-31883 (to R.B. and S.S.). We acknowledge Prof. Andrey Shilnikov for valuable comments and fruitful discussions about neuron models.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • M. Angeles Martínez
    • 1
    Email author
  • Roberto Barrio
    • 1
  • Sergio Serrano
    • 1
  1. 1.Departamento de Matemática Aplicada and IUMAUniversidad de ZaragozaZaragozaSpain

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