Finding Periodic Orbits in the Hindmarsh-Rose Neuron Model
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.
KeywordsPeriodic Orbit Initial Point Newton Method Chaotic Attractor Stable Manifold
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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