Study Of Dynamical Behaviors Of Delayed Complex Neuron Systems Under Noise

In this work, nonlinear dynamical behaviors in delayed neuron systems under noise are studied. It is found that the complexity including internal noise, non-Gaussian noise and channel block is of a constructive role for the dynamical behavior of the complex neuron networks.First, we studied the dynamical behaviors of stochastic Hodgkin–Huxley (HH) neuron networks under internal noise. We found that:(1) Under the internal noise, the spiking behavior of delayed HH neuron networks becomes the most regular at an optimal time delay, indicating the occurrence of delay-induced coherence resonance (CR). Interestingly, there are different CR types, depending on the membrane patch size of the neuron. For smaller patch size, only single CRL occurs; while for larger patch size, coherence bi-resonance (CBR) appears.(2) In the stochastic small-world HH neuron networks, as the delay is increased, the neurons exhibit transitions from spiking synchronization (SS) to clustering anti-phase synchronization (APS) and back to SS. Furthermore, the SS after the APS is enhanced with increasing time delay.Secondly, we studied the dynamical behaviors of complex neuron networks under non-Gaussian noise. We found that:(1) In small-world HH neuron networks with non-Gaussian noise, it is found that, as the delay is increased, the neurons exhibit transitions from irregular spiking to clustering anti-phase synchronization, and then to intermittent multiple temporal coherence and spatial synchronization. It is also found that the spatio-temporal resonances appear when the delay length is roughly integer multiples of the spiking periods, which manifests as the locking between the delay length and the spiking periods.(2) In static scale-free HH neuron networks with non-Gaussian noise, it is found thatτcan induce multiple stochastic resonances and spatial synchronization. Moreover, It is also shown that the resonances are strengthened under appropriate non-Gaussian noise and larger average degree. Furthermore, in BA scale-free modified Hodgkin–Huxley (MHH) neuron networks with non-Gaussian noise, it is found that for electrical synapses, the neurons exhibit a single synchronization transition with time delay and coupling strength, while for chemical synapses, there are multiple synchronization transitions with time delay, and the synchronization transition with coupling strength is dependent on the time delay lengths. For short delays we observe a single synchronization transition, whereas for long delays the neurons exhibit multiple synchronization transitions as the coupling strength is varied. These results show that gap junctions and chemical synapses have different impacts on the pattern formation and synchronization transitions of the scale-free MHH neuronal networks. These findings would be helpful for further understanding the roles of gap junctions and chemical synapses in the firing dynamics of neuronal networks.In the last, we studied the effect of channel block (CB) on spiking activity on delayed stochastic Hodgkin-Huxley neuron networks, it is found that in the absence of CB, time delay-induced multiple CR were observed. In the case of potassium CB, there are also delay-induced multiple CR, but as potassium CB increases, both the time interval between two resonances and the spiking coherence for the resonance decrease, which shows that potassium CB may help delay-induced spiking coherence more frequently reach resonances. In the case of sodium CB, multiple resonances are considerably reduced and turned into single resonance as sodium CB increases, showing that sodium CB deteriorates multiple resonances. For both potassium and sodium CB, the spiking coherence resonance is strengthened as the patch size increases. These findings imply that CB may have subtle effects on the spiking coherence in delayed neuronal networks, and thus should be considered along with time delays in the information processing in real neural system.