Volume 109, Number 2, January 2015
|Number of page(s)||6|
|Published online||27 January 2015|
Symbolic dynamical unfolding of spike-adding bifurcations in chaotic neuron models
1 Departamento de Matemática Aplicada and IUMA, University of Zaragoza - E-50009, Zaragoza, Spain
2 CODY and GME, University of Zaragoza - E-50009, Zaragoza, Spain
3 Laboratoire de Physique des Lasers, Atomes, et Molecules, CNRS, UMR8523, and Université Sciences et Technologies F-59655, Villeneuve d'Ascq, France
Received: 24 October 2014
Accepted: 24 December 2014
We characterize the systematic changes in the topological structure of chaotic attractors that occur as spike-adding and homoclinic bifurcations are encountered in the slow-fast dynamics of neuron models. This phenomenon is detailed in the simple Hindmarsh-Rose neuron model, where we show that the unstable periodic orbits appearing after each spike-adding bifurcation are associated with specific symbolic sequences in the canonical symbolic encoding of the dynamics of the system. This allows us to understand how these bifurcations modify the internal structure of the chaotic attractors.
PACS: 05.45.Ac – Low-dimensional chaos / 05.45.Pq – Numerical simulations of chaotic systems / 87.19.ll – Models of single neurons and networks
© EPLA, 2015
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