Study Of Dynamic Behavior Due To Autaptic Activity And Internalnoise In Neuronal Networks

In this work, the effect of autaptic activity and internal noise on the dynamic behavior of the neuronal network is studied.First of all, we study the effect of the role of autaptic self-feedback activity on the dynamic behavior of the neuronal network with time delay and internal noise. It is find that:1. In Newman–Watts(NW) small-world Hodgkin–Huxley(HH) neuronal network with time delays, the neuronal firing activity exhibit multiple synchronization transitions as chemical autaptic self-feedback delay is varied, and the phenomenon enhances when autaptic self-feedback strength increases. Moreover, this phenomenon becomes strongest when network time delay or coupling strength is optimal. It is also find that the synchronization transitions by network time delay can be enhanced by autaptic activity and become strongest when autaptic self-feedback delay is optimal. These results show that autaptic delayed self-feedback activity can intermittently enhance and reduce the synchronization of the neuronal network and hence plays an important role in regulating the synchronization of the neurons. These findings could find potential implications of autaptic activity for the information processing and transmission in neuronal systems.2. In stochastic NW small-world HH neuronal network with internal noise, chemical autaptic self-feedback delay can induce multiple synchronization transitions and coherence resonance(CR), and synchronicity and periodicity of neuronal firing activity have corresponding relationship. Moreover, multiple CR and synchronization transitions induced by autaptic self-feedback delay enhance when autaptic self-feedback strength increases. When internal noise intensity and network randomness as well as the coupling strength is intermediate, multiple synchronization transitions become strongest and multiple CR enhances when internal noise intensity decreases and network randomness increases as well as the coupling strength increases. These findings show that autaptic activity have a significant effect on the dynamic behavior of the neuronal network with internal noise, and will have an effect on information coding and information processing time precision.Then, we study the effect of internal noise on the dynamic behavior of the neuronal network with time delay. It is find that:In stochastic NW small-world HH neuronal network with time delays, network time delay can induce multiple synchronization transitions only when internal noise intensity is intermediate, and the synchronization transitions become most obvious when internal noise intensity is optimal. When network time delay is constant, neuronal firing activity can also exhibit multiple synchronization transitions as internal noise intensity is varied,and the phenomenon is enhanced when network time delay is tuned at around time delays that can induce synchronization transition. Moreover the phenomenon becomes most obvious when the value of coupling strength and the value of network randomness is optimal. These results show that internal noise has a subtle regulation effect on the synchronization of the neuronal network. These findings may find potential implications for the normal and pathological functions in the brain and the information processing and transmission in neuronal systems.Finally, we study the effect of internal noise and time delay on the dynamic behavior of spike-timing-dependent plasticity(STDP)adaptive neuronal network. It is find that:1. In adaptive NW small-world HH neuronal network with STDP, synchronization transitions induced by autaptic self-feedback delay change when STDP adjusting rate changes and multiple synchronization transitions become most obvious when STDP adjusting rate is optimal.2. In adaptive NW small-world HH neuronal network with STDP, synchronization transitions induced by network delay change when STDP adjusting rate changes and multiple synchronization transitions become most obvious when STDP adjusting rate is optimal.3. In adaptive NW small-world stochastic HH neuronal network with STDP, internal noise could induce CR, and the strength of CR is less than the case of constant coupling. The phenomenon of CR induced by internal noise decreases when STDP adjusting rate increases and the internal noise intensity for CR decreases when STDP adjusting rate increases.These phenomena show that STDP has a significant effect on the dynamic behavior induced by internal noise and autaptic activity in neuronal networks, and thus it could play an important role in information processing and transmission in neural systems.