what does activation function become in spiking neural network? In common ANN, nodes are based on a activation function, like a sigmoid or tanh or ReLU. Updates of synaptic weight are based on the derivative of this function.

When node are represented with spiking neurons, what does activation function become ? how updates of synaptic weight are done ?
The activation function would be inherent to the spiking model used. 

Each model  have a different dynamic which will depend on the proper model and parameters used.