Science China Technological Sciences

, Volume 59, Issue 3, pp 364–370 | Cite as

Enhancement of pacemaker induced stochastic resonance by an autapse in a scale-free neuronal network

  • Ergin YilmazEmail author
  • Veli Baysal
  • Matjaž Perc
  • Mahmut Ozer


An autapse is an unusual synapse that occurs between the axon and the soma of the same neuron. Mathematically, it can be described as a self-delayed feedback loop that is defined by a specific time-delay and the so-called autaptic coupling strength. Recently, the role and function of autapses within the nervous system has been studied extensively. Here, we extend the scope of theoretical research by investigating the effects of an autapse on the transmission of a weak localized pacemaker activity in a scale-free neuronal network. Our results reveal that by mediating the spiking activity of the pacemaker neuron, an autapse increases the propagation of its rhythm across the whole network, if only the autaptic time delay and the autaptic coupling strength are properly adjusted. We show that the autapse-induced enhancement of the transmission of pacemaker activity occurs only when the autaptic time delay is close to an integer multiple of the intrinsic oscillation time of the neurons that form the network. In particular, we demonstrate the emergence of multiple resonances involving the weak signal, the intrinsic oscillations, and the time scale that is dictated by the autapse. Interestingly, we also show that the enhancement of the pacemaker rhythm across the network is the strongest if the degree of the pacemaker neuron is lowest. This is because the dissipation of the localized rhythm is contained to the few directly linked neurons, and only afterwards, through the secondary neurons, it propagates further. If the pacemaker neuron has a high degree, then its rhythm is simply too weak to excite all the neighboring neurons, and propagation therefore fails.


autapse self-delayed feedback neuron channel noise scale-free network 


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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Ergin Yilmaz
    • 1
    Email author
  • Veli Baysal
    • 1
  • Matjaž Perc
    • 2
    • 3
  • Mahmut Ozer
    • 4
  1. 1.Department of Biomedical Engineering, Engineering FacultyBülent Ecevit UniversityZonguldakTurkey
  2. 2.Department of Physics, Faculty of SciencesKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Faculty of Natural Sciences and MathematicsUniversity of MariborMariborSlovenia
  4. 4.Department of Electrical and Electronics Engineering, Engineering FacultyBülent Ecevit UniversityZonguldakTurkey

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