title: Spike timing-dependent plasticity induces non-trivial topology in the brain.
abstract: We study the capacity of Hodgkin-Huxley neuron in a network to change temporarily or permanently their connections and behavior, the so called spike timing-dependent plasticity (STDP), as a function of their synchronous behavior. We consider STDP of excitatory and inhibitory synapses driven by Hebbian rules. We show that the final state of networks evolved by a STDP depend on the initial network configuration. Specifically, an initial all-to-all topology evolves to a complex topology. Moreover, external perturbations can induce co-existence of clusters, those whose neurons are synchronous and those whose neurons are desynchronous. This work reveals that STDP based on Hebbian rules leads to a change in the direction of the synapses between high and low frequency neurons, and therefore, Hebbian learning can be explained in terms of preferential attachment between these two diverse communities of neurons, those with low-frequency spiking neurons, and those with higher-frequency spiking neurons.
authors.affiliation: Pós-Graduação em Ciências, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, Brazil; Departamento de Matemática, Universidade Tecnológica Federal do Paraná, 86812-460, Apucarana, PR, Brazil.
authors.forename: R R
authors.initials: RR
authors.lastname: Borges
authors.affiliation: Pós-Graduação em Ciências, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, Brazil.
authors.forename: F S
authors.initials: FS
authors.lastname: Borges
authors.affiliation: Pós-Graduação em Ciências, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, Brazil.
authors.forename: E L
authors.initials: EL
authors.lastname: Lameu
authors.affiliation: Pós-Graduação em Ciências, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, Brazil; Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, Brazil; Instituto de Física, Universidade de São Paulo, São Paulo, SP, Brazil. Electronic address: antoniomarcosbatista@gmail.com.
authors.forename: A M
authors.initials: AM
authors.lastname: Batista
authors.affiliation: Instituto de Física, Universidade de São Paulo, São Paulo, SP, Brazil.
authors.forename: K C
authors.initials: KC
authors.lastname: Iarosz
authors.affiliation: Instituto de Física, Universidade de São Paulo, São Paulo, SP, Brazil.
authors.forename: I L
authors.initials: IL
authors.lastname: Caldas
authors.affiliation: Department of Mathematical Sciences, University of Essex, Wivenhoe Park, UK.
authors.forename: C G
authors.initials: CG
authors.lastname: Antonopoulos
authors.affiliation: Institute for Complex Systems and Mathematical Biology, University of Aberdeen, SUPA, Aberdeen, UK.
authors.forename: M S
authors.initials: MS
authors.lastname: Baptista
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D001921:Brain / Q000502:physiology*; D006801:Humans; D007858:Learning / Q000502:physiology; D008959:Models, Neurological; D009473:Neuronal Plasticity / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D013569:Synapses / Q000502:physiology
keywords: Network; Plasticity; Synchronization