The Effects Of Time Delay On Burst Synchronization In Neuronal Networks

In this paper,we mainly investigate the effects of time delay on burst synchronization transition in different neuronal networks.Here,Hindmarsh-Rose model have been modelled and two types of synchronization transition have been exhibited.One is synchronization transition via spiking-changing and the other is synchronization transition via change of types.From the numerical results,these two types of synchronization transition can be induced by time delay in different neuronal network and the other parameters including coupling strengths and synaptic types still have an great influence on synchronization transition induced by time delay.Firstly,we consider the synchronization transition induced by time delay in neuronal network with electrical synapses and neuronal network with excitatory-chemical synapses.We can find that time delay can induce intermittent synchronization and synchronization transition via spiking-changing in these neuronal networks.When coupling strength is small,intermittent synchronization can be observed with FHC bursting activity instead of synchronization transitions.When coupling strength is increasing,intermittent synchronization with FHC or FH bursting activity and synchronization transitions via spiking-changing can all be observed.When it comes to neuronal network with inhibitory-chemical synapses,we find that time delay can not only induce intermittent synchronization but also the above two types of synchronization transition.When coupling strength is small,intermittent synchronization can be observed with FHC bursting activity instead of synchronization transitions.When coupling strength is increasing,intermittent synchronization with FHC and FH bursting activity and synchronization transitions via spiking-changing and via change of types can all be observedSecondly,we consider these two types of synchronization transition induced by time delay in hybrid neuronal network and the change of types of synchronization transition is relate with coupling strength and the proportion of hybrid synapses.In this paper,we construct two types of hybrid neuronal networks.One is the hybrid neuronal network with electrical synapses and chemical synapses(The ratio of excitatory-chemical synapses and inhibitory-chemical synapses is four).The other is hybrid neuronal network with excitatory-chemical synapses and inhibitory-chemical synapses.In these hybrid neuronal networks,two types of synchronization transition can be induced by time delay.When coupling strength is small,synchronization transition via spiking-changing can be induced.When coupling strength is large,synchronization transition via change of type can be induced.What's more,the hybrid neuronal networks of small proportion of electrical synapses and inhibitory-chemical synapses can emergent the transition through change of bursting type induced by time delay with large coupling strength.Finally,we consider two types of synchronization transitions induced by double time delay in chemical hybrid neuronal network,where the time delay of excitatory-chemical synapses is different from inhibitory-chemical synapse.With the increasing of coupling strength,synchronous behaviors of the neuronal network will be tend to fade away.When the proportion of inhibitory synapses is small,two types of synchronization transition can be induce by double time delay.When the proportion of inhibitory synapses is increasing gradually,only synchronization transition via change of types can be induce by double time delay.When the proportion of inhibitory synapses is large enough,synchronous behaviors trends to disappear,as well as synchronization transition.In conclusion,two types of synchronization transition can be induce by time delay in different neuronal networks.However,in different neuronal networks,the methods and conditions for time-delay-induced simultaneous transfer are not the same.