Abstract
We study the effects of electrical and chemical autapse on the temporal coherence or firing regularity of single stochastic Hodgkin-Huxley neurons and scale-free neuronal networks. Also, we study the effects of chemical autapse on the occurrence of spatial synchronization in scale-free neuronal networks. Irrespective of the type of autapse, we observe autaptic time delay induced multiple coherence resonance for appropriately tuned autaptic conductance levels in single neurons. More precisely, we show that in the presence of an electrical autapse, there is an optimal intensity of channel noise inducing the multiple coherence resonance, whereas in the presence of chemical autapse the occurrence of multiple coherence resonance is less sensitive to the channel noise intensity. At the network level, we find autaptic time delay induced multiple coherence resonance and synchronization transitions, occurring at approximately the same delay lengths. We show that these two phenomena can arise only at a specific range of the coupling strength, and that they can be observed independently of the average degree of the network.
Highlights
Of pacemaker activity can dramatically be improved with aid of electrical autapse in small-world and scale-free neuronal networks when the imposed rhythms by the autapse, intrinsic dynamics and weak signal are locked
We consider that the HH neuron has an autapse modeled as electrical autapse and add the autaptic current coming from this autaptic self-feedback connection to the neuronal dynamics by means of Eq (13)
With the increasing of κ, while the Coherence resonance (CR) phenomenon enhances and remains approximately stable within the same τ range at both autapse cases, the multiple CR (MCR) phenomenon disappears in the presence of an electrical autapse
Summary
Of pacemaker activity can dramatically be improved with aid of electrical autapse in small-world and scale-free neuronal networks when the imposed rhythms by the autapse, intrinsic dynamics and weak signal are locked. The emergence of multiple CR (MCR) phenomenon induced by information transmission delay and time periodic coupling strength in the presence of channel noise is reported in various theoretical works[22,23,24]. Due to the synchronous oscillations of neurons in the brain are thought to be associated with pathological brain functions including several neural diseases[27,28] and underline many higher order brain functions, such as sensory integration, movement initiation and memory formation[29] much efforts is devoted to the investigation of synchronization phenomena in neuronal networks, and reported many sources inducing synchronization and synchronization transitions in neuronal networks, such as information transmission delay induced synchronization[30,31], synchronization transitions due to time delay, coupling strength and noise[32,33,34,35]. We present detailed results while for details concerning the employed mathematical model and the analysis, we refer the reader to the Methods section further below
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