Effects of time delay and coupling strength on synchronization transitions in excitable homogeneous random network

• Different effects of time delay and coupling strength on synchronization transitions in EHRNs have been discovered.
• Three distinct parameter regions have been found as time delay is increased.
• The phenomenon of multi-stability is observed in the transition region.
• Two different effects of coupling strength on synchronization transitions have been discussed.
• All results revealed in the manuscript are independence on the system size.

In this paper we numerically investigate the effects of time delay and coupling strength on synchronization transitions in excitable homogeneous random network. Different roles of time delay and coupling strength have been discovered by synchronization parameter and space–time plots. Specifically, we have found three distinct parameter regions, i.e., asynchronous region (domain I for small time delay), transition region (domain II for moderate time delay) and synchronous region (domain III for large time delay) as time delay is increased. The phenomenon of multi-stability is observed in the transition region. While coupling strength can enhance synchronization in the transition region and can reduce synchronization time in the synchronous region. All these results are independence on the system size.