### Abstract

Original language | English |
---|---|

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 |

### Fingerprint

### Keywords

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

### Cite this

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*,

*82*(3), 036203. https://doi.org/10.1103/PhysRevE.82.036203

**Combined effect of chemical and electrical synapses in Hindmarsh-Rose neural networks on synchronization and the rate of information.** / Baptista, Murilo Da Silva; Kakmeni, F. Moukam; Grebogi, Celso.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*, vol. 82, no. 3, pp. 036203. https://doi.org/10.1103/PhysRevE.82.036203

}

TY - JOUR

T1 - Combined effect of chemical and electrical synapses in Hindmarsh-Rose neural networks on synchronization and the rate of information

AU - Baptista, Murilo Da Silva

AU - Kakmeni, F. Moukam

AU - Grebogi, Celso

PY - 2010/9/7

Y1 - 2010/9/7

N2 - 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.

AB - 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.

KW - neuronal synchronization

KW - dynamical-systems

KW - metric invariant

KW - mammalian brain

KW - automorphisms

KW - transmission

KW - neocortex

KW - entropy

KW - time

U2 - 10.1103/PhysRevE.82.036203

DO - 10.1103/PhysRevE.82.036203

M3 - Article

VL - 82

SP - 036203

JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

SN - 1539-3755

IS - 3

ER -