No abstract

Rhythmic patterns in the neuronal motifs are studied. For nonequal time-delays without noises, two situations are considered, where the conditions for synchronization, winnerless competition (WLC) and “two plus one” (TPO) are studied. In the first situation, if the coupling strengths are the same, then the time-delays are set the same. WLC and synchronization are easy to occur in this situation, while TPO is hard to occur. In the second situation, if the distances between two neurons are the same, then the time-delays are set the same. The complementary phenomenon is found and discussed in detail for TPO to occur in this situation. Next, when common noise with equal time-delay [Formula: see text] is added to the motifs, noise induced synchronization is compared for [Formula: see text] and [Formula: see text], where the motifs both exhibit WLC. When correlated noises with equal time-delay [Formula: see text] are added to the motifs, it is found that WLC is easier to be destroyed for [Formula: see text] than for [Formula: see text].