Transition of spatiotemporal patterns in neuronal networks with chemical synapses

• Fast excitatory synapse connection is more helpful for the spatiotemporal pattern formation in neuronal network.
• The emergence of regular spatiotemporal patterns is closely related to high fraction of neurons in the firing state.
• Spatiotemporal pattern transitions are connected to sudden changes in the firing complexity of neuronal network.

In mammalian neocortex plane waves, spiral and irregular waves appear alternately. In this paper, we study the transition of spatiotemporal patterns in neuronal networks in which neurons are coupled via two types of chemical synapses: fast excitatory synapse and fast inhibitory synapse. Our results indicate that the fast excitatory synapse connection is easier to induce regular spatiotemporal patterns than fast inhibitory synapse connection, and the mechanism is discussed through bifurcation analysis of a single neuron. We introduce the permutation entropy as a measure of network firing complexity to study the mechanisms of formation and transition of spatiotemporal patterns. Our calculations show that the spatiotemporal pattern transitions are closely connected to a sudden decrease in the firing complexity of neuronal networks, and the neuronal networks with fast excitatory synapses have higher firing complexity than those with fast inhibitory synapses.