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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Regularization of Map-based Neuron Models Using Phase Control

Discontinuity, Nonlinearity, and Complexity 1(1) (2012) 69--78 | DOI:10.5890/DNC.2012.03.001

Javier Used; Alexandre Wagemakers; Miguel A.F. Sanjuán

Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28993Móstoles, Madrid, Spain (E-mail:,,

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Recently discrete dynamical systems, maps, have been also used as valid phenomenological neuron models, and are able to furnish an advantageous alternative to continuous dynamical systems for the modelling of the spiking behavior of single neurons and of neuronal networks as well. Periodic and chaotic spiking, phasic and tonic bursting, subthreshold oscillations and many more specific features of the activity of real neurons can be reproduced by maps with a minimum of analytical complexity. As an external stimulation is applied to the neuron, its response can be of two different natures: periodic or erratic. We present a simple method of control that allows to choose one of the possible responses when the perturbation is periodic. The phase difference between the periodical driving and the control plays a decisive role.


Financial support from the Spanish Ministry of Science and Innovation under Project No. FIS2009-09898 is acknowledged.


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