Chaos in Neural Oscillators Induced by Unidirectional Electrical Coupling

¹ Center for Biomedical Technology, Technical University of Madrid Campus Montegancedo, 28223 Pozuelo de Alarcon, Madrid, Spain
² Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Díaz de Leon Paseos de la Montaña, 47460 Lagos de Moreno, Jalisco, Mexico
³ Centro de Investigaciones en Optica, Loma del Bosque 115 Lomas del Campestre, 37150 Leon, Guanajuato, Mexico

^* Corresponding author. E-mail: alexander.pisarchik@ctb.upm.es

Abstract

We demonstrate that unidirectional electrical coupling between two periodically spiking Hindmarsh-Rose neurons induces bistability in the system. We find that for certain values of intermediate coupling, the slave neuron exhibits coexistence of two attractors. One of them is the periodic orbit similar to the original attractor without coupling, and the other one is a chaotic attractor or a periodic orbit with higher periodicity, depending on the coupling strength. For strong coupling, the slave neuron is monostable at a periodic orbit similar to the attractor of the master neuron. When the master and slave neurons are in a similar attractor they are completely synchronized, whereas being in different states they are in generalized synchronization. We also present the experimental evidence of this behavior with electronic circuits based on the Hindmarsh-Rose model.