### Abstract

In this work we studied the combined action of chemical and electrical synapses in small networks of Hindmarsh-Rose (HR) neurons on the synchronous behavior and on the rate of information produced (per time unit) by the networks. We show that if the chemical synapse is excitatory, the larger the chemical synapse strength used the smaller the electrical synapse strength needed to achieve complete synchronization, and for moderate synaptic strengths one should expect to find desynchronous behavior. Otherwise, if the chemical synapse is inhibitory, the larger the chemical synapse strength used the larger the electrical synapse strength needed to achieve complete synchronization, and for moderate synaptic strengths one should expect to find synchronous behaviors. Finally, we show how to calculate semianalytically an upper bound for the rate of information produced per time unit (Kolmogorov-Sinai entropy) in larger networks. As an application, we show that this upper bound is linearly proportional to the number of neurons in a network whose neurons are highly connected.

Original language | English |
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Pages (from-to) | 036203 |

Number of pages | 12 |

Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |

Volume | 82 |

Issue number | 3 |

DOIs | |

Publication status | Published - 7 Sep 2010 |

### Keywords

- neuronal synchronization
- dynamical-systems
- metric invariant
- mammalian brain
- automorphisms
- transmission
- neocortex
- entropy
- time

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## Cite this

Baptista, M. D. S., Kakmeni, F. M., & Grebogi, C. (2010). Combined effect of chemical and electrical synapses in Hindmarsh-Rose neural networks on synchronization and the rate of information.

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*,*82*(3), 036203. https://doi.org/10.1103/PhysRevE.82.036203