In- and Anti-transition of Firing Patterns Induced by Random Long-range Connections in Coupled Hindmarsh-Rose Neurons System

The effects of random long-range connections （shortcuts） on the transitions of neural firing patterns in coupled Hindmarsh-Rose neurons are investigated, where each neuron is subjected to an external current. It is found that, on one hand, the system can achieve the transition of neural firing patterns from the fewer-period state to the multi-period one, when the number of the added shortcuts in the neural network is greater than a threshold value, indicating the occurrence of in-transition of neural firing patterns. On the other hand, for a stronger coupling strength, we can also find the similar but reverse results by adding some proper random connections. In addition, the influences of system size and coupling strength on such transition behavior, as well as the internality between the transition degree of firing patterns and its critical characteristics for different external stimulation current, are also discussed.