Study Of The Role Of Time-periodic Coupling Strength In The Spiking Behavior Of Neuronal Networks

In this work, spiking behavior of neuronal networks on condition of time-periodiccoupling strength(TPCS) is studied. It is found that internal noise, non-Gaussian noise and timedelay is of a constructive role for the spiking behavior of the complex neuronal networks.First, we studied the effect of TPCS on the spiking coherence of Newman–Watts networksof Hodgkin-Huxley (HH) neuronal networks with non-Gaussian noise. We found that：The spiking can exhibit coherence resonance (CR) when the non-Gaussian noise’sdeviation from Gaussian noise and the amplitude of the coupling strength is varied. Inparticular, coherence bi-resonance (CBR) is observed when the frequency of the couplingstrength is varied, and the CBR always occur when the frequency is equal to or multiple of thespiking period, manifesting as the locking between the frequencies of the spiking and thecoupling strength. These results show that the TPCS may play a more constructive and efficientrole in enhancing the spiking coherence of the neuronal networks compared to the constantcoupling strength. These findings provide insight into the role of TPCS for enhancing the timeprecision of information processing in neuronal networks.Secondly, we studied TPCS induce spiking behavior of stochastic HH neuronal networksunder internal noise. We found that:When the amplitude of TPCS is varied, the spiking induced by channel noise can exhibitCR and CBR, and the CR moves to a smaller patch area (bigger channel noise) when theamplitude increases; when the frequency of TPCS is varied, the intrinsic spiking can exhibitCBR and multiple CR, and the CR always occurs when the frequency is equal to or multiple ofthe spiking period, manifesting as the locking between the frequencies of the intrinsic spikingand the coupling strength.In the last, we studied how the spiking coherence and delay-induced CR changed whenTPCS frequency is varied by employing Newman–Watts HH neuronal networks with TPCS.We found that:The number of delay-induced CR increases with increasing frequency, and when thefrequency is increased to a threshold value there are more CR than that for constant couplingstrength. The spiking can also exhibit multiple CR behavior with the change of TPCSfrequency, and the multiple CR occurs at the frequency approximately multiple of the spiking frequency. Furthermore, the CR occurs at a more precise frequency or time delay for TPCSthan for constant coupling strength. These results show that the spiking temporal coherence canbe repeatedly optimized by TPCS frequency, and time delay can optimize the spikingcoherence more frequently in the case of TPCS. This implies that TPCS could play a moreefficient role than constant coupling strength in improving the time precision of the informationprocessing in delayed neuronal networks.