Study Of Dynamic Behaviors Due To Periodic Coupling Strength In Delayed Neural Network

In this work, nonlinear dynamical behaviors in delayed neuron systems under time-varyingcoupling strength are studied. It is found that the time-periodic coupling strength and theintensity of random fluctuations of increment speed (IS) of adaptive coupling strength are of apositive role for the dynamical behavior of the complex neuron networks.Firstly, we studied the dynamical behaviors of the complex neuron networks under thetime-periodic coupling strength (TPCS).(1) In the effect of TPCS on the synchronization of firing activity in delayed NW networks ofMHH neurons. It is found that time delay can induce more synchronization transitions in thepresence of TPCS compared to fixed coupling strength. In particular, as the frequency ofTPCS is varied, the firing exhibits multiple synchronization transitions depending on thevalues of time delay.(2) In the effect of TPCS on the synchronization of firing activity in delayed SF networks ofMHH neurons. TPCS can also enhance the temporal coherence and spatial synchronization ofthe optimal spatio-temporal bursting. Not only TPCS can increase the synchronizationtransitions by time delay, but also TPCS frequency and network connection degree k caninduce multiple synchronization transitions in the neuronal networks.These results show that TPCS can increase the synchronization transitions by time delay inthe chaotic bursting neuronal networks. This means that TPCS plays an important role andhelp to better understand improving the time precision of the information processing andtransmission in complex neuronal networks.Secondly, we studied the dynamical behaviors of neuron networks under fixed adaptivecoupling strength.In the effect of adaptive coupling on the firing behavior and transitions in time-delay NWnetworks of thermosensitive neurons. With electrical and chemical synapse, time-delayinduced firing behavior and transitions differ significantly. It is found in the case of electricalsynapses, the bursts for a fixed delay involve equal number of spikes in each burst, and forcertain time delays the firing can be inhibited. However, in the case of chemical synapses thebursts for a fixed delay involve different numbers of spikes in each burst, and no firinginhibition is observed. These findings can help to better understand different firing behaviors in complex neuronal networks with electrical and chemical synapses.In the last, we studied the dynamical behaviors of complex neuron networks under IS ofadaptive coupling strength.Based on weighted adaptive scale-free Hodgkin–Huxley neuron network with time delays,it is found that the spiking behavior exhibits synchronization transitions when the intensity ofrandom fluctuations is varied, and the synchronization transitions are delay dependent. It isalso found that the synchronization transitions are reduced when the network connectiondegree increases. These findings provide new insight into the role of randomly changingcoupling strength in the synchronization transitions in neuronal networks. They are expectedto find their potential implications in the information transmission in neural systems.