The spiking neural network (SNN) using leaky-integrated-and-fire (LIF) neurons has been commonly used in automatic speech recognition (ASR) tasks. However, the LIF neuron is still relatively simple compared to that in the biological brain. Further research on more types of neurons with different scales of neuronal dynamics is necessary. Here we introduce four types of neuronal dynamics to post-process the sequential patterns generated from the spiking transformer to get the complex dynamic neuron improved spiking transformer neural network (DyTr-SNN). We found that the DyTr-SNN could handle the non-toy automatic speech recognition task well, representing a lower phoneme error rate, lower computational cost, and higher robustness. These results indicate that the further cooperation of SNNs and neural dynamics at the neuron and network scales might have much in store for the future, especially on the ASR tasks.