Chaos in Neural Oscillators Induced by Unidirectional Electrical Coupling
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 simil...
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| Veröffentlicht in: | Mathematical modelling of natural phenomena 2017-01, Vol.12 (4), p.43-52 |
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| creator | García-Vellisca, M. A. Jaimes-Reátegui, R. Pisarchik, A. N. |
| description | 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. |
| doi_str_mv | 10.1051/mmnp/201712405 |
| format | Article |
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A. ; Jaimes-Reátegui, R. ; Pisarchik, A. N.</creator><contributor>Tyukin, I. ; Gorban, A. ; Makarov, V. ; Osipov, G. ; Makarov, V. ; Gorban, A. ; Osipov, G. ; Tyukin, I.</contributor><creatorcontrib>García-Vellisca, M. A. ; Jaimes-Reátegui, R. ; Pisarchik, A. N. ; Tyukin, I. ; Gorban, A. ; Makarov, V. ; Osipov, G. ; Makarov, V. ; Gorban, A. ; Osipov, G. ; Tyukin, I.</creatorcontrib><description>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. 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| subjects | 37D45 37N25 92B25 92C20 Bistability chaos Circuits Coexistence coherence Coupling Electronic circuits Firing pattern neuron Neurons Oscillators Periodicity Synchronism Synchronization |
| title | Chaos in Neural Oscillators Induced by Unidirectional Electrical Coupling |
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